## Envision Math 5th Grade Textbook Answer Key Topic 20.3 Constructing Shapes

Constructing Shapes

How can you construct congruent triangles?
Triangles are rigid figures which makes them useful in constructing buildings.

Question.
Construct a triangle that is congruent to triangle XYZ.

Another Example
How can you construct a rectangle?
A rectangle has four right angles and opposite sides that are parallel and congruent. Construct a rectangle ABCD
Step 1
Draw a line AB. Construct a line perpendicular to line AB at point A. Choose a point D on the line.

Step 2
Construct a line perpendicular to line AB at point B.

Step 3
Construct a line perpendicular to line AD at point D

Step 4
The point where the perpendicular lines you constructed in Steps 2 and 3 intersect is point C.

Explain It
Question 1.
What are the the four right angles in ABCD?

Question 2.
Name the two pairs of parallel and congruent sides in ABCD

Step 1
Construct ∠P congruent to ∠X.

Step 2
On one side of ∠P, construct $$\overline{P Q}$$ ≅ $$\overline{X Y}$$. On the other side of ∠P, construct $$\overline{P R}$$ ≅ $$\overline{X Z}$$

Step 3
Draw segment QR. ∆PQR ≅ ∆XYZ

Guided Practice

Do you know HOW?
Question 1.
Copy the following triangle on another sheet of paper. Then construct a triangle.

Question 2.
Construct a rectangle using a compass and straightedge.

Do you UNDERSTAND?
Question 3.
When you construct a rectangle, what is the measure of each angle?

Question 4.
How can you be sure that a triangle you construct is congruent to the original triangle?

Independent Practice

Copy each triangle on another sheet of paper. Then construct a triangle congruent to it.
Question 5.

Question 6.

Question 7.

Question 8.
Copy the following line on another sheet of paper. Use it to construct a rectangle.

Question 9.
Ellen studied math for 1$$\frac{1}{2}$$ hours, science for $$\frac{3}{4}$$ hour, and history for $$\frac{3}{4}$$ hour. How many hours did she study in all?

Question 10.
Alan bought 2 packages of tennis balls for $7.98 each. How much change will Alan get from$20?

Question 11.
Geometry What is the measure of the third angle in the triangle?

Question 12.
Algebra Yasmin is 6 inches taller than Burt. If b represents Burt’s height, which expression represents Yasmin’s height?
A. b + 6
B. b × 6
C. b – 6
D. b ÷ 6

Question 13.
Reasoning Terry is arranging furniture and wants to center her 6.5-foot table against a wall that measures 15 feet. How far will the table be from each end of the wall? You can draw a picture to help you.

Question 14.
Squares for a quilt are being cut from a piece of material that is 15 inches wide and 20 inches long. The squares are 4 inches on each side. How many whole squares can be cut from the material? Draw a picture to help you.

Question 15.
Mr. Smith is redecorating his dining room. Tell if he needs to find the perimeter or area for each the following.
a. the amount of wallpaper border to go around the top of the room
b. the amount of carpeting needed to cover the floor

Question 16.
Writing to Explain How can you construct a triangle that is congruent to triangle EFG formed by the roofline of the house?

Question 17.
Let x represent the number of miles Gina ran. Paul ran 3 more than $$\frac{1}{2}$$ many miles as Gina. Which expression represents the distance Paul ran?
A. $$\frac{1}{2}$$(x + 3)
B. $$\frac{1}{2}$$x + 3
C. 3x + $$\frac{1}{2}$$
D. 2(x + 3)

Mixed Problem Solving

Question 1.
How many Kemp’s Ridley sea turtle nests were found in 2002?

Question 2.
How many more Kemp’s Ridley nests were found in 2004 than in 2001?

Question 3.
Is there a trend in the data for Kemp’s Ridley sea turtle nests? Explain.

Question 4.
Between which two years did the number of Kemp’s Ridley nests increase the most?

Question 5.
On a picture graph that shows the number of participants in rubber duck derbies, one picture equals one thousand participants. How many participants are represented by 3.5 pictures?

Question 6.
Strategy Focus Solve using the strategy Use Reasoning. Greg, Rick, and Tom like either math, science, or art best. Tom dislikes art. Rick is not the student who likes art or math best. Which student likes each subject best?

Question 7.
What was the high temperature on August 4?