# Lesson 5

Splitting Triangle Sides with Dilation, Part 1

• Let’s draw segments connecting midpoints of the sides of triangles.

### Problem 1

What is the measure of angle $$A’B’C$$?

A:

$$20^\circ$$

B:

$$40^\circ$$

C:

$$60^\circ$$

D:

$$80^\circ$$

### Problem 2

Triangle $$DEF$$ is formed by connecting the midpoints of the sides of triangle $$ABC$$. The lengths of the sides of $$DEF$$ are shown. What is the length of $$AB$$?

### Problem 3

Angle $$ABC$$ is taken by a dilation with center $$P$$ and scale factor $$\frac13$$ to angle $$A’B’C’$$. The measure of angle $$ABC$$ is $$21^\circ$$. What is the measure of angle $$A’B’C’$$?

(From Unit 3, Lesson 4.)

### Problem 4

Draw 2 lines that could be the image of line $$m$$ by a dilation. Label the lines $$n$$ and $$p$$.

(From Unit 3, Lesson 4.)

### Problem 5

Is it possible for polygon $$ABCDE$$ to be dilated to figure $$VWXYZ$$? Explain your reasoning.

(From Unit 3, Lesson 3.)

### Problem 6

Triangle $$XYZ$$ is scaled and the image is $$X'Y'Z'$$. Write 2 equations that could be used to solve for $$a$$

(From Unit 3, Lesson 2.)

### Problem 7

1. Lin is using the diagram to prove the statement, “If a parallelogram has one right angle, it is a rectangle.” Given that $$EFGH$$ is a parallelogram and angle $$HEF$$ is a right angle, write a statement that will help prove angle $$FGH$$ is also a right angle.
2. Han then states that the 2 triangles created by diagonal $$EG$$ must be congruent. Help Han write a proof that triangle $$EHG$$ is congruent to triangle $$GFE$$.
(From Unit 2, Lesson 12.)