## Envision Math 5th Grade Textbook Answer Key Topic 20 Reteaching

**Reteaching**

**Set A, pages 452-453**

Construct an angle congruent to angle A.

Answer:

Draw a ray with endpoint E.

With point A as center, use your compass to draw an arc that intersects both sides of angle A. Label the points of intersection R and S. With the same compass setting, use point E as center and draw an arc that intersects the ray at point D.

Open the compass to length RS. Then, with point D as center, draw an intersecting arc.

Label the intersection F. Use a straightedge to draw ray EF.

Angle E is congruent to angle A.

**Remember** that a construction uses only a compass and a straightedge.

Construct an angle congruent to the given angle.

Question 1.

Answer:

Question 2.

Answer:

**Set B, pages 454-456**

Construct a line perpendicular to another line.

Answer:

- Draw line AB.
- With A as center, draw two arcs that intersect line AB. Label the points of intersection D and E.
- Open the compass wider.
- Using D and E as centers, draw arcs that intersect. Label the intersection C.
- Draw Line CA.
- Line CA is perpendicular to line AB.

**Remember** to keep the compass open to the same setting when drawing the arcs with D and E as the centers.

Question 1.

Construct a line perpendicular to another line.

Answer:

Question 2.

For the construction started below, what is the next step to construct a line perpendicular to line XY?

Answer:

**Set C, pages 458-460**

Construct a triangle congruent to triangle DEF.

Answer:

- Draw a ray with endpoint G.
- Construct angle G.
- Congruent to angle D.
- Construct segments GK and GL on the sides of angle G so that they are congruent to segments DE and DF.
- Draw segment KL.
- Triangle GKL is congruent to triangle DEF.

Construct a rectangle ABCD.

Answer:

- Draw line AB.
- Construct line DA perpendicular to line AB at A.
- Construct line DC perpendicular to line DA at D.
- Construct line CB perpendicular to line AB at B.
- Lines DC and CB intersect at C.

**Remember** to use the compass to measure the length of the original line segments by placing the point on one endpoint and the slider on the other endpoint.

Question 1.

Construct a triangle congruent to triangle XYZ.

Answer:

Question 2.

Construct a rectangle KLMN.

Answer:

**Set D, pages 462-463**

When you use objects to solve problems, follow these steps.

Step 1: Choose objects that can best model what is described in the problem.

Step 2: Use the objects to make a model of what you know.

Step 3: Use the objects to act out the action in the problem. Look for patterns.

Step 4: Find the answer in your model.

**Remember** to state clearly at the beginning what your objects represent in the problem.

Question 1.

How many total bricks are needed if the pattern extends to 4 bricks in the middle row?

Answer: