{"id":12199,"date":"2023-12-15T09:19:13","date_gmt":"2023-12-15T03:49:13","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=12199"},"modified":"2023-12-16T09:22:47","modified_gmt":"2023-12-16T03:52:47","slug":"envision-math-common-core-grade-5-answer-key-topic-16","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-5-answer-key-topic-16\/","title":{"rendered":"enVision Math Common Core Grade 5 Answer Key Topic 16 Geometric Measurement: Classify Two-Dimensional Figures"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 5 Answer Key<\/a>\u00a0Topic 16 Geometric Measurement: Classify Two-Dimensional Figures<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 5th Grade Answers Key Topic 16 Geometric Measurement: Classify Two-Dimensional Figures<\/h2>\n

\"Envision
\nenVision STEM Project: Ecosystems<\/strong>
\nDo Research Use the Internet or other sources to learn more about ecosystems. Look for examples of changes that living organisms might cause. List three different ecosystems and describe any changes that humans might have made to each one.
\nJournal: Write a Report Include what you found. Also in your report:
\n\u2022 Compare two ecosystems. List 10 living things and 5 non-living things you might find in each one.
\n\u2022 Think about changes that can occur in an ecosystem. Are the changes positive or negative? Why?
\n\u2022 Use two-dimensional shapes to make a map or diagram of an ecosystem.<\/p>\n

Review What You Know<\/strong><\/p>\n

A-Z Vocabulary<\/strong><\/p>\n

Choose the best term from the box. Write it on the blank.<\/p>\n

\u2022 degree
\n\u2022 polygon
\n\u2022 line segment
\n\u2022 quadrilateral
\n\u2022 parallel
\n\u2022 vertex
\n\u2022 perimeter<\/p>\n

Question 1.
\nA ___ is a polygon with four sides.<\/p>\n

Answer:
\nA quadrilateral is a polygon with four sides.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA quadrilateral is a polygon with four sides.
\nfor example:
\nsquare is a quadrilateral.
\nsquare has four sides of equal length.
\nsquare has four internal right angles.
\nso a quadrilateral is a polygon with four sides.<\/p>\n

Question 2.
\nThe point where two sides of a polygon intersect is a ___<\/p>\n

Answer:
\nThe point where two sides of a polygon intersect is a vertex.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point where two sides of a polygon intersect is a vertex.
\nfor example:
\ntriangle is a polygon.
\na polygon with three sides is a triangle.
\nwe name a triangle by its three vertices.
\nso the point where two sides of a polygon intersect is a vertex.<\/p>\n

\"Two-Dimensional<\/p>\n

Question 3.
\nThe distance between ____ sides of a polygon is always the same.<\/p>\n

Answer:
\nThe distance between parallel sides of a polygon is always the same.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe distance between the number of sides of a polygon is always the same.
\nfor example:
\nthe rectangle is a polygon.
\nthe rectangle has opposite sides that are equal.
\nso the distance between parallel sides of a polygon is always the same.<\/p>\n

Question 4.
\nThe ____ is a unit of measure for angles.<\/p>\n

Answer:
\nA degree is a unit of measure for angles.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na degree is a unit of measure for angles.
\nfor example:
\na circle is divided into 360 equal degrees.
\nso that a right angle is 90 degrees.
\nso the degree is a unit of measure for angles.<\/p>\n

Decimals<\/strong>
\nFind each answer.<\/p>\n

Question 5.
\n2.75 + 9.08<\/p>\n

Answer:
\n2.75 + 9.08 = 11.83.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\naddition of two numbers.
\nthe numbers are 2.75 and 9.08.
\n2.75 + 9.08.
\n11.83.<\/p>\n

Question 6.
\n17.6 – 3.08<\/p>\n

Answer:
\n17.6 – 3.08 = 14.52.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nsubtraction of two numbers.
\nthe numbers are 17.6 and 3.08.
\n17.6 – 3.08.
\n14.52.<\/p>\n

Question 7.
\n83.2 \u00d7 0.1<\/p>\n

Answer:
\n83.2 x 0.1 = 8.32.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nmultiplication of two numbers.
\nthe numbers are 83.2 and 0.1.
\n83.2 x 0.1.
\n8.32.<\/p>\n

Question 8.
\n24.27 \u00d7 103<\/sup><\/p>\n

Answer:
\n24.27 x 1000 = 24270.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nmultiplication of two numbers.
\nthe numbers are 24.27 and 10 x 10 x 10.
\n10 x 10 x 10 = 1000.
\n24.27 x 1000 = 24270.<\/p>\n

Fractions<\/strong>
\nFind each answer.<\/p>\n

Question 9.
\n3\\(\\frac{2}{3}\\) + 6\\(\\frac{9}{10}\\)<\/p>\n

Answer:
\n3(2\/3) + 6(9\/10) = 7.2.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\naddition of two numbers.
\nthe numbers are 3(2\/3) and 6(9\/10).
\n2\/3 = 0.6.
\n9\/10 = 0.9.
\n3(0.6) + 6(0.9).
\n1.8 + 5.4 = 7.2.
\n3(2\/3) + 6(9\/10) = 7.2.<\/p>\n

Question 10.
\n8\\(\\frac{1}{2}\\) – 4\\(\\frac{4}{5}\\)<\/p>\n

Answer:
\n8(1\/2) – 4(4\/5) = 0.8.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nsubtraction of two numbers.
\nthe numbers are 8(1\/2) and 4(4\/5).
\n1\/2 = 0.5.
\n4\/5 = 0.8.
\n8(0.5) – 4(0.8).
\n4 – 3.2 = 0.8.
\n8(1\/2) – 4(4\/5) = 0.8.<\/p>\n

\"Two-Dimensional<\/p>\n

Question 11.
\n8 \u00f7 \\(\\frac{1}{2}\\)<\/p>\n

Answer:
\n8 \u00f7 \\(\\frac{1}{2}\\) = 16.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\ndivision of two numbers.
\nthe numbers are 8 and 1\/2.
\n8 \/ 0.5.
\n16.
\n8 \u00f7 \\(\\frac{1}{2}\\) = 16.<\/p>\n

Question 12.
\n\\(\\frac{1}{3}\\) \u00f7 6<\/p>\n

Answer:
\n\\(\\frac{1}{3}\\) \u00f7 6 = 0.05.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\ndivision of two numbers.
\nthe numbers are 6 and 1\/3.
\n1\/3 = 0.3.
\n0.3 \/ 6 = 0.05.
\n\\(\\frac{1}{3}\\) \u00f7 6 = 0.05.<\/p>\n

Write an Equation<\/strong><\/p>\n

Question 13.
\nLouisa drew a polygon with six sides of equal length. If the perimeter of Louisa’s polygon is 95.4 centimeters, how long is each side? Use an equation to solve.<\/p>\n

Answer:
\nThe length of each side = 15.9 cm.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nIf the perimeter of Louisa’s polygon is 95.4 centimeters.
\na polygon with 6 sides is called a hexagon.
\nperimeter of hexagon = 6a.
\nwhere a = side.
\np = 6 a.
\n95.4 = 6 a.
\na = 95.4 \/ 6.
\na = 15.9 cm.
\nso the length of each side = 15.9 cm.<\/p>\n

Question 14.
\nThe area of a rectangle is 112 square inches. If the length of the rectangle is 16 inches, what is the width of the rectangle? Use an equation to solve.<\/p>\n

Answer:
\nThe width of the rectangle is = 7 in.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe area of a rectangle is 112 square inches.
\nIf the length of the rectangle is 16 inches.
\narea of the rectangle = l x w.
\nwhere l = length and w = width.
\n112 = 16 x w.
\n112 \/16 = w.
\nw = 7.
\nso the width of the rectangle = 7 in.<\/p>\n

Pick a Project<\/strong><\/p>\n

PROJECT 16A<\/strong>
\nWhere can you find a pyramid?
\nProject: Build a Pyramid
\n\"Envision<\/p>\n

PROJECT 16B<\/strong>
\nHow do blueprints use different shapes?
\nProject: Draw a Blueprint
\n\"Envision<\/p>\n

PROJECT 16C<\/strong>
\nWhat shapes make up a map?
\nProject: Hunt for Shapes in a Map
\n\"Envision<\/p>\n

PROJECT 16D<\/strong>
\nWhat does the Florida flag look like?
\nProject: Design a Flag
\n\"Envision<\/p>\n

Answer:
\nThe Florida flag looks like a cross mark.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nin the flag, has the cross mark.
\nthe cross mark is inside the flag.
\nso the Florida flag looks like a cross mark.
\ncross mark indicates it is not correct.<\/p>\n

Lesson 16.1 Classify Triangles<\/h3>\n

Solve & Share<\/strong>
\nOne triangle is shown below. Draw five more triangles with different properties. Next to each triangle, list its properties such as 2 equal sides, 1 right angle, 3 acute angles, and so on. Work with a partner to solve this problem.<\/p>\n

In a triangle, angles will be either acute, right, or obtuse.
\n\"Envision<\/p>\n

Look Back! Reasoning<\/strong> What are some different ways you can put triangles into categories? Explain.<\/p>\n

Answer:
\nThey are acute, obtuse, equilateral, right triangles.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe equilateral triangle has all the sides equal length.
\nan acute triangle is a trigon with three sides and three angles each less than 90 degrees.
\nan obtuse triangle will have one and only one obtuse angle.
\nthe other two angles are acute angles.
\na right triangle is a triangle in which one angle is a right angle.
\nan isosceles triangle has at least two sides of the same length.
\nso the triangles are acute, obtuse, equilateral, right triangles.<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong> How Can You Classify Triangles?<\/p>\n

A.<\/strong>
\nTriangles can be classified by the lengths of their sides.
\n\"Envision
\nEquilateral triangle All sides are the same length.<\/p>\n

\"Envision
\nIsosceles triangle At least two sides are the same length.<\/p>\n

\"Envision
\nScalene triangle No sides are the same length<\/p>\n

Can you tell if the sides of a triangle are the same length without measuring them?
\n\"Envision<\/p>\n

The total measure of all the angles in a triangle is 180\u00b0.
\n\"Envision<\/p>\n

B.<\/strong>
\nTriangles can also be classified by the measures of their angles.
\n\"Envision
\nRight triangle One angle is a right angle.
\n\"Envision
\nAcute triangle All three angles are acute angles.
\n\"Envision
\nObtuse triangle One angle is an obtuse angle.<\/p>\n

Convince Me! Construct Arguments<\/strong> Can you draw an equilateral right triangle? Explain using precise mathematical language.<\/p>\n

To justify a mathematical argument, you must use precise mathematical language and ideas to explain your thinking
\n\"Envision<\/p>\n

Answer:
\nYes, we can draw an equilateral right triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nwe can draw an equilateral triangle with 90 degrees.
\nright angle means it has 90 degrees.
\nan equilateral triangle has all the sides are equal.
\nso we can draw an equilateral right triangle.<\/p>\n

Guided Practices<\/strong><\/p>\n

Do You Understand?<\/strong><\/p>\n

Question 1.
\nCan a right triangle have an obtuse angle? Why or why not?<\/p>\n

Answer:
\nNo, the right triangle has an obtuse angle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe right triangle cannot be an obtuse angle.
\nsince a right-angled triangle has one right angle, the other two angles are acute.
\ntherefore, an obtuse-angled triangle can never have a right angle.
\nthe side opposite the obtuse angle in a triangle is the longest.
\nso the right triangle is not an obtuse angle.<\/p>\n

Question 2.
\nCan an equilateral triangle have only two sides of equal length? Why or why not?<\/p>\n

Answer:
\nNo, an equilateral triangle has only two sides of equal length.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nan equilateral triangle has all three sides are equal.
\nif only two sides are equal in length, then it is an isosceles triangle.
\nso the equilateral triangle does not have only two sides of equal length.<\/p>\n

Do You Know How?<\/strong><\/p>\n

In 3 and 4, classify each triangle by its sides and then by its angles.<\/p>\n

Question 3.
\n\"Envision<\/p>\n

Answer:
\nThe triangle is an equilateral triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe three angles are equal.
\nthe three sides are equal sides.
\nan equilateral triangle has all the sides are equal.
\nso the triangle is an equilateral triangle.<\/p>\n

Question 4.
\n\"Envision<\/p>\n

Answer:
\nThe triangle is an isosceles triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two sides have an equal length.
\nthey are 7 inches.
\nthe other side is 9.9 in.
\nan isosceles triangle has only two sides are equal.
\nso the above triangle is an isosceles triangle.<\/p>\n

Independent Practice<\/strong><\/p>\n

In 5-10, classify each triangle by its sides and then by its angles.<\/p>\n

Question 5.
\n\"Envision<\/p>\n

Answer:
\nThe above triangle is an acute-angle triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two sides and the two sides have the same length.
\nthey are 75 degrees and 6 in.
\nthe other side has a different side length.
\nacute angle triangle has two equal lengths.
\nso the above triangle is an acute-angled triangle.<\/p>\n

Question 6.
\n\"Envision<\/p>\n

Answer:
\nThe triangle is a scalene triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe triangle has three sides.
\nthe three sides have three different lengths.
\na scalene triangle has different lengths.
\nso the above-given triangle is a scalene triangle.<\/p>\n

Think about what you need to compare to classify the triangle correctly.
\n\"Envision<\/p>\n

Question 7.
\n\"Envision<\/p>\n

Answer:
\nThe triangle is an equilateral triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe triangle has the 3 equal sides and three equal angles.
\n60 + 60 + 60 = 180.
\nan equilateral triangle has all three sides equal in length.
\nso the above triangle is an equilateral triangle.<\/p>\n

Question 8.
\n\"Envision<\/p>\n

Answer:
\nThe triangle is an obtuse-angled triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe triangle has 2 equal sides.
\nobtuse-angled triangle has only two equal side lengths.
\nso the triangle is an obtuse-angled triangle.<\/p>\n

Question 9.
\n\"Envision<\/p>\n

Answer:
\nThe triangle is a scalene triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe triangle has three different side lengths.
\nthe side lengths are 6m, 10m, and 8m.
\na scalene triangle has three different side lengths.
\nso the triangle is a scalene triangle.<\/p>\n

Question 10.
\n\"Envision<\/p>\n

Answer:
\nThe triangle is an isosceles triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe triangle has two different side lengths.
\nthey are 12 cm and 6.5 cm.
\nan isosceles triangle has the two sides equal.
\nso the triangle is an isosceles triangle.<\/p>\n

Problem Solving<\/strong><\/p>\n

Question 11.
\nThe Louvre Pyramid serves as an entrance to the Louvre Museum in Paris. The base of the pyramid is 35 meters long and the sides are 32 meters long. Classify the triangle on the front of the Louvre Pyramid by the lengths of its sides and the measures of its angles.
\n\"Envision<\/p>\n

Answer:
\nThe Louvre triangle is in the shape of an isosceles triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe Louvre Pyramid serves as an entrance to the Louvre Museum in Paris.
\nThe base of the pyramid is 35 meters long and the sides are 32 meters long.
\nan isosceles triangle has two equal side lengths.
\nthe other side is a difference in length.
\nso the Louvre triangle is in the shape of an isosceles triangle.<\/p>\n

Question 12.
\nA pizza is divided into twelve equal slices. Glenn and Ben each ate \\(\\frac{1}{6}\\) of the pizza on Monday. The next day Ben ate \\(\\frac{1}{2}\\) of the pizza that was left over. How many slices of the original pizza remain? Explain your reasoning.<\/p>\n

Answer:
\nThe number of slices of the original pizza remains = 2 pieces.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA pizza is divided into twelve equal slices.
\nGlenn and Ben each ate \\(\\frac{1}{6}\\) of the pizza on Monday.
\nThe next day Ben ate \\(\\frac{1}{2}\\) of the pizza that was leftover.
\n1\/6 + 1\/2.
\n1\/6 = 0.16.
\n1\/2 = 0.5.
\n0.16 + 0.5 = 0.66.
\nso the number of slices of the original pizza remains = 2 pieces.<\/p>\n

Question 13.
\nDuring a sale at the bookstore, books sold for $3 and magazines sold for $2.50. Jan spent $16 and bought a total of 6 books and magazines. How many of each did she buy?<\/p>\n

Answer:
\nThe number of each did she buy = $17.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nDuring a sale at the bookstore, books sold for $3, and magazines sold for $2.50.
\nJan spent $16 and bought a total of 6 books and magazines.
\n6 x 3 = $18.
\n6 x $2.50 = $15.
\n$18 + $15 = 33.
\n$33 – $16 = $17.
\nso the number of each did she buy = $17.<\/p>\n

Question 14.
\nHigher Order Thinking<\/strong> The measures of two angles of a triangle are 23\u00b0 and 67\u00b0. Is the triangle acute, right, or obtuse? Use geometric terms in your explanation.<\/p>\n

Answer:
\nThe triangle is an acute-angled triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe measures of two angles of a triangle are 23\u00b0 and 67\u00b0.
\nthe triangles have two different angles.
\nthey are 23\u00b0 and 67\u00b0.
\nso the triangle is an acute-angled triangle.<\/p>\n

Question 15.
\nMake Sense and Persevere<\/strong> An animal shelter houses dogs, cats, and rabbits. There are 126 animals at the shelter. Of the animals, \\(\\frac{1}{3}\\) are cats. Three fourths of the remaining animals are dogs. How many of the animals are rabbits? Show your work.<\/p>\n

Answer:
\nThe number of animals is rabbits = 21.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAn animal shelter houses dogs, cats, and rabbits.
\nThere are 126 animals at the shelter.
\nOf the animals, \\(\\frac{1}{3}\\) are cats.
\nThree-fourths of the remaining animals are dogs.
\n1\/3 = 0.3.
\n3\/4 = 0.75.
\n0.3 + 0.75 = 1.05.
\nso the number of animals is rabbits = 21.<\/p>\n

Assessment Practice<\/strong><\/p>\n

Question 16.
\nTwo sides of a triangle measure 5 inches and 6 inches. Jason says the triangle must be scalene. Is Jason correct? Explain.<\/p>\n

Answer:
\nNo, Jason is not correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nTwo sides of a triangle measure 5 inches and 6 inches.
\na scalene triangle has all three sides have different lengths.
\nan isosceles triangle has the two sides are equal.
\nso Jason is not correct.<\/p>\n

Lesson 16.2 Classify Quadrilaterals<\/h3>\n

Solve & Share<\/strong>
\nDraw any length line segment that will fit in the space below. The line segment can go in any direction, but it must be straight. Draw another line segment of any length that is parallel to the first one. Connect the ends of each line segment with line segments to make a closed four-sided figure. What does your shape look like? Can you classify it? Discuss your ideas with a partner.<\/p>\n

Answer:
\nThe shape looks like is a rectangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe line segment has 5 cm in length.
\nthe other line segment has the same 2 cm in length.
\nso the lines joined is formed a rectangle.
\nthe rectangle has two opposite sides that are equal.
\nthe rectangle has the area = length x width.
\nso the shape looks like a rectangle.<\/p>\n

You can use reasoning to find the differences and similarities between shapes when classifying quadrilaterals. Show your work!
\n\"Envision<\/p>\n

Look Back! Reasoning<\/strong> How can you draw a quadrilateral different from the one above? Describe what you can change and why it changes the quadrilateral.<\/p>\n

Answer:
\nThe quadrilateral formed is square.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe line segment is increased by 3 cm.
\n5 – 2 = 3.
\nso it has 4 equal side lengths.
\narea of the square = 4 s.
\nwhere S = sides.
\nso the quadrilateral formed is square.<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong> What Are Some Properties of Quadrilaterals?
\nA.<\/strong>
\nCategories of quadrilaterals are classified by their properties.
\n\u2022 How many pairs of opposite sides are parallel?
\n\u2022 Which sides have equal lengths?
\n\u2022 How many right angles are there?<\/p>\n

Think about the questions below when you are classifying quadrilaterals.
\n\"Envision<\/p>\n

B.<\/strong>
\nA trapezoid has one pair of parallel sides.
\n\"Envision
\nA parallelogram has two pairs of opposite sides parallel and equal in length.
\n\"Envision<\/p>\n

C.<\/strong>
\nA rectangle has four right angles.
\n\"Envision
\nA rhombus has all sides the same length.
\n\"Envision<\/p>\n

D.<\/strong>
\nA square has all sides the same length.
\n\"Envision
\nA square has four right angles.<\/p>\n

Convince Me! Generalize<\/strong> How is a parallelogram different from a rhombus? How are they similar?<\/p>\n

Guided Practice<\/strong><\/p>\n

Do You Understand?<\/strong><\/p>\n

Question 1.
\nA-Z Vocabulary<\/strong> How are a square and a rhombus alike?<\/p>\n

Answer:
\nYes, a square and a rhombus have four equal sides.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe square has four sides of the same length.
\nsquare has four right angles.
\nrhombus has all sides the same length.
\nso the square and a rhombus have four equal sides.<\/p>\n

Question 2.
\nVocabulary<\/strong> How is a trapezoid different from a parallelogram?<\/p>\n

Answer:
\nYes, both of them are different.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na trapezoid has one pair of parallel sides.
\na parallelogram has two pairs of opposite sides and is equal in length.
\nso both of them are different.<\/p>\n

Do You Know How?<\/strong><\/p>\n

In 3-6, use as many names as possible to identify each polygon. Tell which name is most specific.<\/p>\n

Use the questions at the top of page 626 to help you classify the quadrilaterals.
\n\"Envision<\/p>\n

Question 3.
\n\"Envision<\/p>\n

Answer:
\nThe quadrilateral is a square.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe quadrilateral has 4 equal sides.
\nfour right angles.
\nso the square has 4 equal sides.
\nso the quadrilateral is a square.<\/p>\n

Question 4.
\n\"Envision<\/p>\n

Answer:
\nThe quadrilateral is a rectangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe quadrilateral has opposite equal sides.
\nfour right angles.
\nso the rectangle has opposite equal sides.
\nso the quadrilateral is a rectangle.<\/p>\n

Question 5.
\n\"Envision<\/p>\n

Answer:
\nThe quadrilateral is a rhombus.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe quadrilateral has 4 equal sides.
\nso the rhombus has 4 equal sides.
\nso the quadrilateral is a rhombus.<\/p>\n

Question 6.
\n\"Envision<\/p>\n

Answer:
\nThe quadrilateral is a parallelogram.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe quadrilateral has opposite sides are equal.
\nfour right angles.
\nso the rectangle has opposite equal sides.
\nso the quadrilateral is a parallelogram.<\/p>\n

Independent Practice<\/strong><\/p>\n

Question 7.
\nIdentify the polygon using as many names as possible.
\n\"Envision<\/p>\n

Answer:
\nThe polygon is a square and rhombus.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe polygon has 4 equal sides.
\nthe polygon has 4 equal angles.
\nso the polygon is a square and rhombus.<\/p>\n

Question 8.
\nIdentify the polygon using as many names as possible.
\n\"Envision<\/p>\n

Answer:
\nThe polygon is a quadrilateral and trapezoid.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe polygon has 4 different sides.
\nthe polygon has one right angle.
\nso the polygon is a quadrilateral and trapezoid.<\/p>\n

Question 9.
\nWhy is a square also a rectangle?<\/p>\n

Answer:
\nYes, a square is also a rectangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe square has 4 equal right angles.
\nthe rectangle has 4 equal right angles.
\nso square and rectangle are the same.
\nso the square is also a rectangle.<\/p>\n

Question 10.
\nWhich special quadrilateral is both a rectangle and a rhombus? Explain how you know.<\/p>\n

Answer:
\nThe special quadrilateral is a square.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe square is a rectangle.
\nsquare has 4 equal right angles.
\nrectangle also has 4 equal right angles.
\nrhombus also has 4 equal right angles.
\nso the special quadrilateral is a square.<\/p>\n

Problem Solving<\/strong><\/p>\n

Question 11.
\nEach time Sophie makes a cut to a polygon, she can make a new type of polygon. What kind of polygon is left if Sophie cuts off the top of the isosceles triangle shown?
\n\"Envision<\/p>\n

Answer:
\nThe polygon formed is a trapezoid.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nEach time Sophie makes a cut to a polygon, she can make a new type of polygon.
\nthe polygon is an isosceles triangle.
\nafter Sophie makes a cut to a polygon.
\nso the polygon formed is a trapezoid.<\/p>\n

Question 12.
\nNumber Sense<\/strong> Donald’s car gets about 30 miles per gallon. About how many miles can Donald drive on 9.2 gallons of gas? At $3.15 a gallon, about how much would that amount of gas cost?<\/p>\n

Answer:
\nThe amount of gas cost = $869.4 miles.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nDonald’s car gets about 30 miles per gallon.
\n9.2 x 30 = 276 miles.
\n276 x $3.15 = $869.4 miles.
\nso the amount of gas cost = $869.4 miles.<\/p>\n

Question 13.
\nIs it possible to draw a quadrilateral that is not a rectangle but has at least one right angle? Explain.<\/p>\n

Answer:
\nYes, it is possible to draw a quadrilateral that is not a rectangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe square is also a quadrilateral.
\nsquare has 4 equal right angles.
\nsquare has 4 equal side lengths.
\nso it is possible to draw a quadrilateral that is not a rectangle.<\/p>\n

Question 14.
\nThe area of a quadrilateral is 8.4 square feet. Find two decimals that give a product close to 8.4.<\/p>\n

Answer:
\nThe two decimals are 2.1 and 4.0.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe area of a quadrilateral is 8.4 square feet.
\narea = l x w.
\nwhere l = 2.1 and w = 4.0.
\narea = 2.1 x 4.0.
\narea = 8.4.
\nso the two decimals are 2.1 and 4.0.<\/p>\n

Question 15.
\nBe Precise<\/strong> Suppose you cut a square into two identical triangles. What type of triangles will you make?<\/p>\n

Answer:
\nThe triangle I make is the isosceles triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nSuppose you cut a square into two identical triangles.
\nan isosceles triangle has the two sides equal.
\nthe triangle formed is the isosceles triangle.
\nso the triangle I can make is an isosceles triangle.<\/p>\n

Question 16.
\nHigher Order Thinking<\/strong> A parallelogram has four sides that are the same length. Is it a square? Explain how you know.<\/p>\n

What do you know about the sides of a parallelogram?
\n\"Envision<\/p>\n

Assessment Practice<\/strong><\/p>\n

Question 17.
\nWhich quadrilateral could have side lengths 1 m, 5 m, 1 m, 5 m?
\nA. square
\nB. rectangle
\nC. trapezoid
\nD. rhombus<\/p>\n

Answer:
\nOption B is the correct answer.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe quadrilateral could have side lengths 1 m, 5 m, 1 m, and 5 m.
\nthe rectangle has the opposite sides equal.
\nso option B is the correct answer.<\/p>\n

Question 18.
\nWhich of the following statements is NOT true?
\nA. A rectangle is also a parallelogram.
\nB. A trapezoid is also a quadrilateral.
\nC. A rhombus is also a rectangle.
\nD. A square is also a rectangle.<\/p>\n

Answer:
\nOption C is the correct answer.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na rectangle is also a parallelogram.
\na trapezoid is also a quadrilateral.
\na square is also a rectangle.
\na rhombus is not a rectangle.
\nrhombus has all four equal sides.
\nso option C is the correct answer.<\/p>\n

Lesson 16.3 Continue to Classify Quadrilaterals<\/h3>\n

Solve & Share<\/strong>
\nLook at the quadrilaterals below. In the table, write the letters for all the figures that are trapezoids. Then do the same with each of the other quadrilaterals. Work with a partner to solve this problem.
\n\"Envision<\/p>\n

You can classify quadrilaterals that have more than one property. Show your work!
\n\"Envision<\/p>\n

List the letter of each figure in each group.
\n\"Envision<\/p>\n

Answer:
\nThe number of trapezoids is Q, R, S, U, and O.
\nparallelograms are L, M, and N.
\nthe rectangle is G.
\nthe rhombus is V.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe number of trapezoids is Q, R, S, U, and O.
\nparallelograms are L, M, and N.
\nthe rectangle is G.
\nthe rhombus is V.<\/p>\n

Look Back! Construct Arguments<\/strong> which quadrilateral had the most figures listed? Explain why this group had the most.<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong>
\nHow Are Special Quadrilaterals Related to Each Other?<\/p>\n

A.<\/strong>
\nThis Venn diagram shows how special quadrilaterals are related to each other.<\/p>\n

How can you use the Venn diagram to describe other ways to classify a square? What does the diagram show about how a trapezoid relates to other special quadrilaterals?<\/p>\n

\"Envision<\/p>\n

B.<\/strong>
\nEach circle in the Venn diagram shows a category of quadrilateral.
\nItems in overlapping sections of the Venn diagram belong to more than one group.
\n“Square\u201d is in more than one circle in the Venn diagram.
\n\"Envision
\nA square is also a rectangle, rhombus, parallelogram, and quadrilateral.<\/p>\n

C.<\/strong>
\nIn the diagram, the circle for trapezoids does not intersect with any other circles. This shows that a trapezoid is also a quadrilateral, but never a parallelogram, rectangle, rhombus, or square.<\/p>\n

Convince Me! Construct Arguments<\/strong> When can a rectangle be a rhombus? Can a rhombus be a rectangle? Explain using examples.<\/p>\n

Guided Practice<\/strong><\/p>\n

Do You Understand?<\/strong><\/p>\n

Question 1.
\nExplain how the Venn diagram on page 630 shows that every rectangle is a parallelogram.<\/p>\n

Answer:
\nYes, every rectangle is a parallelogram.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nsquare is a rectangle, parallelogram, rhombus, and quadrilateral.
\nsquare is also a rectangle.
\nsquare has 4 equal right angles.
\na rectangle has 4 equal right angles.
\nso every rectangle is a parallelogram.<\/p>\n

Question 2.
\nHow are a rectangle and a rhombus alike?<\/p>\n

Answer:
\nThe rectangle and rhombus are alike when they have 4 equal right angles.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nsquare is a rectangle, parallelogram, rhombus, and quadrilateral.
\nsquare is also a rectangle.
\nsquare has 4 equal right angles.
\na rectangle has 4 equal right angles.
\nso every rectangle is a parallelogram.
\nrhombus also have 4 equal right angles.
\nso the rectangle and rhombus are alike.<\/p>\n

Do You Know How?<\/strong><\/p>\n

In 3-6, tell whether each statement is true or false. If false, explain.<\/p>\n

Question 3.
\nAll rectangles are squares.<\/p>\n

Answer:
\nYes, all rectangles are squares.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe square is a rectangle.
\nsquare has 4 equal right angles.
\nrectangles have 4 equal right angles.
\nso all rectangles are squares.<\/p>\n

Question 4.
\nEvery rhombus is a parallelogram.<\/p>\n

Answer:
\nYes, the rhombus is a parallelogram.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na rhombus has 4 equal sides lengths.
\nrhombus has 4 equal right angles.
\na parallelogram has opposite sides equal.
\nso the rhombus is a parallelogram.<\/p>\n

Question 5.
\nParallelograms are special rectangles.<\/p>\n

Answer:
\nParallelograms are special rectangles.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nrectangles have two opposite side lengths.
\nthe parallelogram has two opposite side lengths.
\nso parallelograms are special rectangles.<\/p>\n

Question 6.
\nA trapezoid can be a square.<\/p>\n

Answer:
\nNo, the trapezoid cannot be a square.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe square has 4 sides.
\ntrapezoid also has 4 sides.
\nsquare has all sides equal.
\na trapezoid has all sides not equal.
\nso trapezoid is not a square.<\/p>\n

Independent Practice<\/strong><\/p>\n

In 7-10, write whether each statement is true or false. If false, explain why.<\/p>\n

Question 7.
\nAll rhombuses are rectangles.<\/p>\n

Answer:
\nFalse.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na rhombus has 4 equal side lengths.
\nrectangles have 2 opposite side lengths.
\nso the statement is not correct.<\/p>\n

Question 8.
\nEvery trapezoid is a quadrilateral.<\/p>\n

Answer:
\nYes, the trapezoid is a quadrilateral.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe trapezoid is also a quadrilateral but never a parallelogram, rectangle, rhombus, or square.
\nso the trapezoid is a quadrilateral.<\/p>\n

Question 9.
\nRhombuses are special parallelograms.<\/p>\n

Answer:
\nYes, the rhombus is a special parallelogram.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na rhombus has 4 equal sides.
\nparallelograms have 4 sides.
\nso rhombus is a special parallelogram.<\/p>\n

Question 10.
\nAll rectangles are quadrilaterals.<\/p>\n

Answer:
\nThe statement is not correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nrectangles have two opposite side lengths.
\nthe quadrilateral has two opposite side lengths.
\nso the statement is not correct.<\/p>\n

Question 11.
\nWhat properties does the shape have? Why is it not a parallelogram?
\n\"Envision<\/p>\n

Answer:
\nThe shape formed is a rhombus.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe shape formed is a rhombus.
\nrhombus has 4 equal side lengths.
\nrhombus has 4 equal right angles.
\nso the shape formed is a rhombus.<\/p>\n

Question 12.
\nWhy is a square also a rhombus?<\/p>\n

Answer:
\nYes, a square is also a rhombus.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na square has 4 equal sides.
\nsquare has 4 equal right angles.
\nrhombus has 4 equal sides.
\nrhombus has 4 equal right angles.
\nso the square is also a rhombus.<\/p>\n

Problem Solving<\/strong><\/p>\n

Question 13.
\nConstruct Arguments Draw a quadrilateral with one pair of parallel sides and two right angles. Explain why this figure is a trapezoid.<\/p>\n

Answer:
\nYes, it is a trapezoid.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na trapezoid has one pair of parallel sides and two right angles.
\na quadrilateral with one pair of parallel sides and two right angles.
\nso the figure formed is a trapezoid.<\/p>\n

Question 14.
\nA reflecting pool is shaped like a rhombus with a side length of 6 meters. What is the perimeter of the pool? Explain how you found your answer.
\nThink about the properties of a rhombus to help you solve.
\n\"Envision<\/p>\n

Answer:
\nThe perimeter of the pool is<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA reflecting pool is shaped like a rhombus with a side length of 6 meters.
\nthe perimeter of rhombus = 6 a.
\nwhere a = sides.
\nperimeter = 6 x 6.
\nperimeter = 36 sq m.
\nso the perimeter of the pool is 36 sq m.<\/p>\n

Question 15.
\nA bakery sold 31 bagels in the first hour of business and 42 bagels in the second hour. If the bakery had 246 bagels to start with, how many bagels were left after the second hour?
\nimg 42.7<\/p>\n

Answer:
\nThe number of bagels was left after the second hour = 3.36 bagels.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA bakery sold 31 bagels in the first hour of business and 42 bagels in the second hour.
\nIf the bakery had 246 bagels to start with.
\n42 + 31 = 73.
\n246\/73 = 3.36.
\nso the number of bagels were left after the second hour = 3.36 bagels.<\/p>\n

Question 16.
\nHigher Order Thinking<\/strong> Ann says the figure below is a square. Pablo says that it is a parallelogram. Felix says that it is a rectangle. Can they all be right? Explain.
\n\"Envision<\/p>\n

Answer:
\nAnn was correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe figure has 4 equal sides.
\nthe figures have 4 equal angles.
\nthe above figure is a square.
\nso Ann was correct.<\/p>\n

Assessment Practice<\/strong><\/p>\n

Question 17.
\nBelow is the Venn diagram of quadrilaterals.
\n\"Envision
\nPart A<\/strong>
\nAre rhombuses also rectangles? Explain.
\nPart B<\/strong>
\nWhat are all of the names that describe a rhombus?<\/p>\n

Answer:
\nSquares and rectangles describe a rhombus.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nrhombuses, squares, and rectangles are over-linked with each other.
\nsquare has 4 equal side lengths.
\nsquare has 4 equal right angles.
\nrectangles have 2 opposite equal sides.
\nrhombus has 4 equal side lengths.
\nso squares and rectangles describe a rhombus.<\/p>\n

Lesson 16.4 Construct Arguments<\/h3>\n

Activity<\/strong><\/p>\n

Problem Solving<\/strong><\/p>\n

Solve & Share<\/strong>
\nAlfie thinks that if he cuts a parallelogram along a diagonal, he will get two triangles that have the same shape and size. Is he correct? Solve this problem any way you choose. Construct a math argument to justify your answer.
\n\"Envision<\/p>\n

Answer:
\nThe two triangles are Scalene triangles.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAlfie thinks that if he cuts a parallelogram along a diagonal.
\nhe will get two triangles that have the same shape and size.
\nthe triangles formed are scalene triangles.
\na scalene triangle has 3 different side lengths.<\/p>\n

Thinking Habits<\/strong>
\nBe a good thinker! These questions can help you.
\n\u2022 How can I use numbers, objects, drawings, or actions to justify my argument?
\n\u2022 Am I using numbers and symbols correctly?
\n\u2022 Is my explanation clear and complete?
\n\u2022 Can I use a counterexample in my argument?
\n\"Envision<\/p>\n

Look Back! Construct Arguments<\/strong> Suppose you cut along a diagonal of a rhombus, a rectangle, or a square. Would you get two triangles that have the same shape and size? Construct an argument to justify your answer.<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong> How Can You Construct Arguments?<\/p>\n

A.<\/strong>
\nAnika says, “If I draw a diagonal in a parallelogram, I will always form two right triangles.\u201d Is she correct? Construct a math argument to justify your answer.
\n\"Envision<\/p>\n

You can construct an argument using what you know about triangles and quadrilaterals.
\n\"Envision<\/p>\n

What do I need to do to solve the problem?
\nI need to examine several cases, including special parallelograms. Then I need to state my conclusion and write a good argument to justify it.<\/p>\n

Here’s my thinking..
\n\"Envision<\/p>\n

B.<\/strong>
\nHow can I construct an argument?
\nI can
\n\u2022 use math to explain my reasoning
\n\u2022 use the correct words and symbols.
\n\u2022 give a complete explanation.
\n\u2022 use a counterexample in my argument.<\/p>\n

C.<\/strong>
\nAnika is incorrect. The triangles are right triangles only when the parallelogram is a rectangle or square. Rectangles and squares have four right angles. So, each triangle formed by drawing a diagonal will have a right angle and be a right triangle. But if the parallelogram does not have right angles, each triangle will not have a right angle.
\n\"Envision<\/p>\n

Convince Me! Construct Arguments<\/strong> How can counterexamples be helpful in constructing an argument?<\/p>\n

Guided Practice<\/strong><\/p>\n

Jamal says, \u201cTwo equilateral triangles that are the same size can be joined to make a rhombus.”<\/p>\n

Question 1.
\nWhat is the definition of an equilateral triangle? What is the definition of a rhombus?
\n\"Envision<\/p>\n

Answer:
\nYes, two equilateral triangles that are the same size can be joined to make a rhombus.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nan equilateral triangle has all three sides has an equal length.
\nrhombus has all 4 sides are equal.
\nrhombus has all 4 equal right angles.
\nso the two equilateral triangles that are the same size can be joined to make a rhombus.<\/p>\n

Question 2.
\nHow could knowing these definitions help in constructing your argument?
\nAnswer:<\/p>\n

Question 3.
\nIs Jamal correct? Construct an argument to justify your answer.<\/p>\n

Answer:
\nYes, Jamal was correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nan equilateral triangle has all three sides has an equal length.
\nrhombus has all 4 sides are equal.
\nrhombus has all 4 equal right angles.
\nso the two equilateral triangles that are the same size can be joined to make a rhombus.<\/p>\n

Independent Practice<\/strong><\/p>\n

Construct Arguments<\/strong>
\nLauren says, “If I draw a diagonal in a trapezoid, neither of the triangles formed will have a right angle.”<\/p>\n

Stuck? Answering this question might help. Have I interpreted all word meanings correctly?
\n\"Envision
\nA diagram can help you construct arguments.<\/p>\n

Question 4.
\nWhat is the definition of a trapezoid?<\/p>\n

Answer:
\nThe trapezoid is a quadrilateral with one pair of parallel sides.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe trapezoid is a quadrilateral with one pair of parallel sides.
\narea of trapezoid = 1\/2(a + b) h.
\nwhere a and b are the bases.
\nh is the height.<\/p>\n

Question 5.
\nDraw examples of a diagonal in a trapezoid.<\/p>\n

Answer:
\nThe shape formed is a triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nif the trapezoid is divided into two equal halves.
\nwe can get the two triangles.
\nso the shape formed is a triangle.<\/p>\n

Question 6.
\nHow can you use a drawing to construct an argument?
\nAnswer:<\/p>\n

Question 7.
\nIs Lauren correct? Construct a math argument to justify your answer.
\nAnswer:<\/p>\n

Problem Solving<\/strong><\/p>\n

Performance Task<\/strong>
\nFlag Making<\/strong>
\nMr. Herrera’s class is studying quadrilaterals. The class worked in groups, and each group made a “quadrilateral flag.”
\n\"Envision<\/p>\n

Question 8.
\nConstruct Arguments<\/strong> Which flags show parallelograms? Construct a math argument to justify your answer.<\/p>\n

Answer:
\nFlag 1 shows a parallelogram.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMr. Herrera’s class is studying quadrilaterals.
\nThe class worked in groups, and each group made a “quadrilateral flag.
\nin 1st flag there are parallelograms.
\nso flag 1 shows a parallelogram.<\/p>\n

Question 9.
\nReasoning<\/strong> Explain how you would classify the quadrilaterals on the green flag and the blue flag.<\/p>\n

Answer:<\/p>\n

The definitions of the different quadrilaterals will help you construct arguments.
\n\"Envision<\/p>\n

Question 10.
\nCritique Reasoning<\/strong> Marcia’s group made the red flag. Bev’s group made the orange flag. Both girls say their flag shows all rectangles. Critique the reasoning of both girls and explain who is correct.<\/p>\n

Answer:<\/p>\n

Question 11.
\nMake Sense and Persevere<\/strong> Does it make sense for this quadrilateral to be on any of the flags?
\n\"Envision
\nAnswer:<\/p>\n

Topic 16 Fluency Practice<\/h3>\n

Activity<\/strong><\/p>\n

Point & Tally<\/strong><\/p>\n

Find a partner. Get paper and a pencil. Each partner chooses light blue or dark blue.
\nAt the same time, Partner 1 and Partner 2 each point to one of their black numbers. Both partners find the product of the two numbers.
\nThe partner who chose the color where the product appears gets a tally mark. Work until one partner has seven tally marks.<\/p>\n

\"Envision<\/p>\n

Topic 16 Vocabulary Review<\/strong><\/p>\n

Understand Vocabulary<\/strong><\/p>\n

Word List<\/strong>
\n\u2022 acute triangle
\n\u2022 equilateral triangle
\n\u2022 isosceles triangle
\n\u2022 obtuse triangle
\n\u2022 parallelogram
\n\u2022 rectangle
\n\u2022 rhombus
\n\u2022 right triangle
\n\u2022 scalene triangle
\n\u2022 square
\n\u2022 trapezoid<\/p>\n

Choose the best term from the Word List. Write it on the blank.<\/p>\n

Question 1.
\nA 3-sided polygon with at least two sides the same length is a(n) _____<\/p>\n

Answer:
\nA 3-sided polygon with at least two sides of the same length is a(n) is an equilateral triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na 3-sided polygon with at least two sides of the same length is a(n) is an equilateral triangle.
\nfor example:
\nan equilateral triangle has three sides that are all the same length and three angles that all measure 60 degrees.<\/p>\n

Question 2.
\nA polygon with one pair of parallel sides is a(n) ____<\/p>\n

Answer:
\nA polygon with one pair of parallel sides is a(n) is a trapezium.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na polygon with one pair of parallel sides is a(n) is a trapezium.
\nfor example:
\nif the polygon has one pair of parallel sides is a trapezoid.<\/p>\n

Question 3.
\nA(n) ____ has four right angles and all four sides the same length.<\/p>\n

Answer:
\nA(n) rhombus has four right angles and all four sides the same length.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na(n) rhombus has four right angles and all four sides the same length.
\nfor example:
\na rhombus is a parallelogram with 4 sides of equal length.
\narea of rhombus = 6 a.
\nwhere a = sides.<\/p>\n

Question 4.
\nAll three sides of a(n) ____ are different lengths.<\/p>\n

Answer:
\nAll three sides of a(n) are scalene triangle are different lengths.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAll three sides of a(n) are scalene triangle are different lengths.
\nfor example:
\na scalene triangle is a triangle in which all three sides have different lengths.<\/p>\n

Question 5.
\nThe measure of each of the three angles in a(n) ____ is less than 90\u00b0<\/p>\n

Answer:
\nThe measure of each of the three angles in a(n) acute angle triangle is less than 90\u00b0.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe measure of each of the three angles in a(n) acute angle triangle is less than 90\u00b0.
\nfor example:
\nan acute angle triangle has three angles that each measure less than 90 degrees.<\/p>\n

Question 6.
\nA rectangle is a special type of ____<\/p>\n

Answer:
\nA rectangle is a special type of parallelogram.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na rectangle is a special type of parallelogram.
\nfor example:
\na rectangle is a special case of a parallelogram in which each pair of adjacent sides is perpendicular.<\/p>\n

For each of these terms, draw an example and a non-example.<\/p>\n

\"Envision<\/p>\n

Answer:
\nAn obtuse triangle is an isosceles triangle.
\nRhombus with no right angle is a quadrilateral.
\nAn isosceles right triangle is two equal sides.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAn obtuse triangle is an isosceles triangle.
\nRhombus with no right angle is a quadrilateral.
\nAn isosceles right triangle is two equal sides.<\/p>\n

Use Vocabulary in Writing<\/strong><\/p>\n

Question 10.
\nAlana claims that not all 4-sided polygons with 2 pairs of equal sides are parallelograms. Is Alana correct? Use terms from the Word List in your answer.<\/p>\n

Answer:
\nNo, she is not correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAlana claims that not all 4-sided polygons with 2 pairs of equal sides are parallelograms.
\n2 pairs of equal sides are not parallelograms.
\nso she was not correct.<\/p>\n

Topic 16 Reteaching<\/h3>\n

Set A<\/strong>
\npages 621-624
\nClassify the triangle by the measures of its angles and the lengths of its sides.
\nSince one of the angles is right, this is a right triangle. Since two of the sides are the same length, this is an isosceles triangle.
\n\"Envision
\nIt is a right, isosceles triangle.<\/p>\n

Remember<\/strong> that right, obtuse, and acute describe the angles of a triangle. Equilateral, scalene, and isosceles describe the sides of a triangle.<\/p>\n

Classify each triangle by the measures of its angles and the lengths of its sides.<\/p>\n

Question 1.
\n\"Envision<\/p>\n

Answer:
\nThe triangle is an equilateral triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe triangles have 3 equal sides and three equal angles.
\nso the triangle is an equilateral triangle.<\/p>\n

Question 2.
\n\"Envision<\/p>\n

Answer:
\nThe triangle is a scalene triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe triangle has 3 different sides.
\nthey are 3 in, 5 in, and 4 in.
\nthe three side lengths are different.
\nso the triangle is a scalene triangle.<\/p>\n

Question 3.
\n\"Envision<\/p>\n

Answer:
\nThe triangle is an isosceles triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe triangle has 2 sides of equal length.
\nthey are 8cm and 8 cm.
\nso the triangle is an isosceles triangle.<\/p>\n

Question 4.
\n\"Envision<\/p>\n

Answer:
\nThe triangle is a scalene triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe triangle has 3 different sides.
\nthey are 16.4 cm, 16 cm, and 10 cm.
\nso the triangle is a scalene triangle.<\/p>\n

Set B<\/strong>
\npages 625-628<\/p>\n

Quadrilaterals are classified by their properties.
\nA trapezoid has one pair of parallel sides.
\n\"Envision
\nA parallelogram has two pairs of equal parallel sides.
\n\"Envision
\nA rectangle is a parallelogram with 4 right angles.
\n\"Envision
\nA rhombus is a parallelogram with 4 equal sides.
\n\"Envision
\nA square is a parallelogram with 4 right angles and 4 equal sides.
\n\"Envision<\/p>\n

Remember<\/strong> that some quadrilaterals can be identified by more than one name.<\/p>\n

Identify each quadrilateral. Describe each quadrilateral by as many names as possible.<\/p>\n

Question 1.
\n\"Envision<\/p>\n

Answer:
\nThe quadrilateral is a rectangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe polygon has 4 right angles.
\nthe polygon with 4 right angles is a rectangle.
\nso the quadrilateral is a rectangle.<\/p>\n

Question 2.
\n\"Envision<\/p>\n

Answer:
\nThe quadrilateral is a rhombus.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe polygon has 4 equal sides.
\nrhombus is a parallelogram with 4 equal sides.
\nso the quadrilateral is a rhombus.<\/p>\n

Question 3.
\n\"Envision<\/p>\n

Answer:
\nThe polygon is a trapezoid.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe quadrilateral has 4 sides.
\na trapezoid has one pair of parallel sides.
\nso the polygon is a trapezoid.<\/p>\n

Question 4.
\n\"Envision<\/p>\n

Answer:
\nThe polygon is a square.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe quadrilateral has 4 equal sides and 4 equal angles.
\na square is a parallelogram with 4 right angles and 4 equal sides.
\nso the polygon is a square.<\/p>\n

Set C<\/strong>
\npages 629-632
\nThis Venn diagram shows how special quadrilaterals are related to each other.
\n\"Envision<\/p>\n

Remember<\/strong> that each circle of the Venn diagram shows a subgroup of quadrilaterals.<\/p>\n

Tell whether each statement is true or false.<\/p>\n

Question 1.
\nAll squares are rectangles.<\/p>\n

Answer:
\nTrue.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nall squares are rectangles.
\nsquare is a rectangle.
\narea of the square = 4s.<\/p>\n

Question 2.
\nEvery parallelogram is a rectangle.<\/p>\n

Answer:
\nFalse.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na rectangle is a parallelogram.
\nbut every parallelogram is a rectangle.
\nso the statement is false.<\/p>\n

Question 3.
\nRhombuses are special parallelograms.<\/p>\n

Answer:
\nTrue.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nrhombuses are special parallelograms.
\nrhombus is a special parallelogram.
\narea of the rhombus = 4 a.<\/p>\n

Question 4.
\nAll trapezoids are quadrilaterals.<\/p>\n

Answer:
\nFalse.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na trapezoid is not a quadrilateral.
\nso the above statement is false.<\/p>\n

Set D<\/strong>
\npages 633-636
\nThink about these questions to help you construct arguments.<\/p>\n

Thinking Habits<\/strong>
\n\u2022 How can I use numbers, objects, drawings, or actions to justify my argument?
\n\u2022 Am I using numbers and symbols correctly?
\n\u2022 Is my explanation clear and complete?
\n\u2022 Can I use a counterexample in my argument?
\n\"Envision<\/p>\n

Remember<\/strong> that using definitions of geometric figures can help you construct arguments. Malcolm says, “The sum of the angle measures in any rectangle is 180\u00b0.”<\/p>\n

Question 1.
\nWhat is the definition of a rectangle?<\/p>\n

Answer:
\nA rectangle is a parallelogram with 4 right angles.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na rectangle is a parallelogram with 4 right angles.
\narea of the rectangles = length x width.<\/p>\n

Question 2.
\nDraw a picture of a rectangle and label its angles.<\/p>\n

Answer:
\nA rectangle is a parallelogram with 4 right angles.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na rectangle is a parallelogram with 4 right angles.
\narea of the rectangles = length x width.<\/p>\n

Question 3.
\nIs Malcolm correct? Construct a math argument to justify your answer.
\nAnswer:<\/p>\n

Topic 16 Assessment Practice<\/h3>\n

Question 1.
\nWhich of the following correctly describes the triangles? Select all that apply.
\n\"Envision
\n\"Envision Both triangles have a right angle.
\n\"Envision Only one triangle is a right triangle.
\n\"Envision Only one triangle has an acute angle.
\n\"Envision Both triangles have an obtuse angle.
\n\"Envision Both triangles have at least two acute angles.<\/p>\n

Answer:
\nOnly one triangle is a right triangle.
\nonly one triangle has an acute angle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthere are two triangles.
\nthey have only one triangle is a right triangle.
\nonly one triangle has an acute angle.<\/p>\n

Question 2.
\nWhich statement is true?
\nA. Trapezoids are parallelograms.
\nB. A square is always a rectangle.
\nC. A rectangle is always a square.
\nD. A rhombus is a trapezoid.<\/p>\n

Answer:
\nOption B is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na square is always a rectangle.
\nsquare has 4 equal right angles.
\nthe rectangle has 4 equal right angles.<\/p>\n

Question 3.
\nSelect all the shapes that are parallelograms.
\n\"Envision<\/p>\n

Answer:
\nOption 4 is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe shapes are hexagon, rectangle, trapezoid, and parallelogram.
\nso option 4 is correct.<\/p>\n

Question 4.
\nThe necklace charm shown has one pair of m parallel sides. What type of quadrilateral is the charm? Explain.
\n\"Envision<\/p>\n

Answer:
\nThe charm is in the shape of a trapezoid.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe necklace charm shown has one pair of m parallel sides.
\na trapezoid has one pair of parallel sides.
\nthe above charm has one pair of parallel sides.
\nso the charm is in the shape of a trapezoid.<\/p>\n

Question 5.
\nIdentify the figure below using as many names as possible.
\n\"Envision<\/p>\n

Answer:
\nThe figure is a rhombus.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe square has 4 equal sides and 4 equal angles.
\nrhombus has 4 equal sides.
\nso the figure is a rhombus.<\/p>\n

Question 6.
\nClaim 1: A square is a rectangle because it has 4 right angles.
\nClaim 2: A square is a rhombus because it has 4 equal sides.
\nWhich claim is correct? Explain.<\/p>\n

Answer:
\nYes, both of them are correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na square is a rectangle because it has 4 right angles.
\na square is a rhombus because it has 4 equal sides.
\nso both of them are correct.<\/p>\n

Assessment Practice<\/strong><\/p>\n

Question 7.
\nLook at the rhombus and square below.
\n\"Envision
\nA. How are the two figures the same?
\nB. How are the two figures different?<\/p>\n

Answer:
\nThey are the same when they have 4 equal sides.
\nThey are different when they have 4 equal right angles.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na square is a rectangle because it has 4 right angles.
\na square is a rhombus because it has 4 equal sides.
\nthey are the same when they have 4 equal sides.
\nthey are different when they have 4 equal right angles.<\/p>\n

Question 8.
\nIdentify the figure below using as many names as possible.
\n\"Envision<\/p>\n

Answer:
\nThe polygon is a trapezoid.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe figure has 4 different sides.
\nso the polygon is a trapezoid.<\/p>\n

Question 9.
\nIdentify the figure below using as many names as possible.
\n\"Envision<\/p>\n

Answer:
\nThe polygon is a parallelogram.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe figure has opposite sides equal lengths.
\nparallelogram also has the opposite sides equal lengths.
\nso the polygon is a parallelogram.<\/p>\n

Question 10.
\nWhat shape has two pairs of opposite sides that are parallel and has all sides of equal length but does NOT have four right angles?
\nA. Square
\nB. Rectangle
\nC. Rhombus
\nD. Trapezoid<\/p>\n

Answer:
\nOption C is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nrhombus has two pairs of opposite sides that are parallel.
\nall sides of equal length but do not have 4 right angles.
\nso option C is correct.<\/p>\n

Question 11.
\nUse the Venn diagram. Are rhombuses always, sometimes, or never also parallelograms? Explain.
\n\"Envision<\/p>\n

Answer:
\nRhombuses are always a parallelogram.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nrhombuses are parallelograms.
\nrhombus is a parallelogram with 4 equal sides.
\narea of the rhombus = 4 a.
\nwhere a = side.
\nso rhombuses are always a parallelogram.<\/p>\n

Question 12.
\nDescribe triangle HJK in terms of its sides and angles.
\n\"Envision<\/p>\n

Answer:
\nThe triangle is an isosceles triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\ntriangle HJK is an isosceles triangle.
\nan isosceles triangle has 2 sides equal.
\nso the triangle HJK is an isosceles triangle.<\/p>\n

Topic 16 Performance Task<\/h3>\n

Geometry in Art<\/strong>
\nArtists often use triangles and quadrilaterals in their pictures.<\/p>\n

Question 1.
\nUse the Poster to answer the following questions.
\nPart A<\/strong>
\nClassify Triangle 1 in the Poster by its angles and by its sides.
\n\"Envision<\/p>\n

Answer:
\nThe triangle is a scalene triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\ntriangle 1 is a scalene triangle.
\na scalene triangle has three different sides.<\/p>\n

Part B<\/strong>
\nWhat are all of the names you can use to describe Shape 2 in the Poster?<\/p>\n

Answer:
\nShape 2 is a parallelogram.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nshape 2 is a parallelogram.
\na parallelogram has two pairs of equal parallel sides.
\nshape 2 is a parallelogram.<\/p>\n

Part C<\/strong>
\nTriangles 3 and 4 are identical. They are joined in the Poster to form a square. Construct a math argument to show why Triangles 3 and 4 are isosceles right triangles.
\nPart D<\/strong>
\nIf Triangle 3 is joined with another triangle that is the same size and shape, do the two triangles always form a square? Construct a math argument to explain your reasoning.
\nPart E<\/strong>
\nWhat are the measures of the angles of Triangle 3? Note that two angles in an isosceles triangle always have the same measure. Explain.<\/p>\n

Answer:
\nTriangle 3 is a rhombus.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\ntriangle 3 is a rhombus.
\nin the rhombus, there are 2 equilateral triangles.
\ntriangles 3 and 4 are equilateral triangles.
\nso triangle 3 is a rhombus.<\/p>\n

Question 2.
\nClassify the triangles and quadrilaterals in the Houses drawing to answer the following questions.
\nPart A<\/strong>
\nAre all the triangles shown in the design isosceles? Are they all equilateral? Construct a math argument, using properties, to explain why or why not.
\n\"Envision<\/p>\n

Answer:
\nYes, the triangles are equilateral and isosceles triangle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthere are equilateral and isosceles triangles.
\nan equilateral triangle has all the 3 sides are equal.
\nan isosceles triangle has only two sides that are equal.
\nso the triangles are both equilateral and isosceles triangle.<\/p>\n

Part B<\/strong>
\nAll of the quadrilaterals in the Houses drawing are rectangles. Does that mean all of the quadrilaterals are parallelograms? Does that mean all are squares? Construct a math argument, using properties, to explain your reasoning.<\/p>\n

Answer:
\nYes, all of the quadrilaterals in the house drawing are rectangles.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nall of the quadrilaterals in the house drawing are rectangles.
\nall the quadrilaterals are parallelograms.
\nall squares are rectangles.
\nso all of the quadrilaterals in the house drawing are rectangles.<\/p>\n","protected":false},"excerpt":{"rendered":"

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