# Lesson 12

Similar Polygons

Let’s look at sides and angles of similar polygons.

### Problem 1

Triangle $$DEF$$ is a dilation of triangle $$ABC$$ with scale factor 2. In triangle $$ABC$$, the largest angle measures $$82^\circ$$. What is the largest angle measure in triangle $$DEF$$?

A:

$$41^\circ$$

B:

$$82^\circ$$

C:

$$123^\circ$$

D:

$$164^\circ$$

### Problem 2

Draw two polygons that are similar but could be mistaken for not being similar. Explain why they are similar.

### Problem 3

Draw two polygons that are not similar but could be mistaken for being similar. Explain why they are not similar.

### Problem 4

These two triangles are similar. Find side lengths $$a$$ and $$b$$. Note: the two figures are not drawn to scale.

### Problem 5

Jada claims that $$B’C’D’$$ is a dilation of $$BCD$$ using $$A$$ as the center of dilation.

What are some ways you can convince Jada that her claim is not true?

(From Unit 2, Lesson 9.)

### Problem 6

1. Draw a horizontal line segment $$AB$$.

2. Rotate segment $$AB$$ $$90^\circ$$ counterclockwise around point $$A$$. Label any new points.
3. Rotate segment $$AB$$ $$90^\circ$$ clockwise around point $$B$$. Label any new points.
4. Describe a transformation on segment $$AB$$ you could use to finish building a square.
(From Unit 1, Lesson 7.)