## Envision Math 5th Grade Textbook Answer Key Topic 20.1 Constructing Angles

**Review What You Know**

**Vocabulary**

Choose the best term from the box.

Question 1.

A ? extends in two directions infinitely.

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Question 2.

A ? has one endpoint and extends in one direction, while a ? has two endpoints.

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Question 3.

? lines intersect at one point and create four right angles.

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**Identifying Angles**

Classify each angle as acute, obtuse, straight or right.

Question 4.

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Question 5.

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Question 6.

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Question 7.

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**Patterns**

Find the next two numbers in each pattern.

Question 8.

1.5, 1.7, 1.9, 2.1,2.3, ☐, ☐

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Question 9.

26, 21,16, 11, ☐, ☐

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Shapes

Writing to Explain Write an answer for each question.

Question 10.

Can a triangle have two obtuse angles?

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Question 11.

Is a square always a rectangle?

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**Constructing Angles**

How can you construct an angle congruent to another angle?

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A geometric construction is the drawing of a figure using only a compass and a straightedge. A ruler and a protractor are not used in making a construction.

Question.

How would you construct ∠*B *congruent to ∠*M*?

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**Guided Practice**

**Do you know HOW?**

In 1 and 2, trace each angle on a sheet of paper. Then construct an angle congruent to each given angle.

Question 1.

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Question 2.

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**Do you UNDERSTAND?**

Question 3.

Writing to Explain Why is it important to keep the same compass setting in Step 1?

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Question 4.

How can you tell if a constructed angle is congruent to the original angle?

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**Independent Practice**

In 5 through 7, trace each angle on a sheet of paper. Then construct an angle congruent to each given angle

Question 5.

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Question 6.

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Question 7.

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**Problem Solving**

Question 8.

The Leaning Tower of Pisa is located in Italy. It leans to the south at the angle shown in the picture below. Construct an angle congruent to ∠A.

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Question 9.

Mario has saved a number of quarters, nickels, dimes, and pennies. He will use $3.93 to buy a new toy for his dog. Using the fewest coins, what combination of coins will equal $3.93?

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Question 10.

Justin climbed 15 steps to the second floor of a building. Each step is 8 inches high. How many feet higher is the second floor than the first?

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Question 11.

Diamond cutters must cut angles precisely so that the greatest amount of light is reflected from the facets. Refer to the photo of the diamond below. Construct an angle congruent to ∠W.

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Question 12.

The high temperatures in a city for 7 days were 87°, 87°, 90°, 90°, 90°, 92°, and 87°. What was the mean temperature for the 7 days?

A. 87°

B. 89°

C. 90°

D. 91°

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