# Lesson 8

Similar Triangles

### Problem 1

In each pair, some of the angles of two triangles in degrees are given. Use the information to decide if the triangles are similar or not. Explain how you know.

• Triangle A: 53, 71, ___; Triangle B: 53, 71, ___

• Triangle C: 90, 37, ___; Triangle D: 90, 53, ___

• Triangle E: 63, 45, ____; Triangle F: 14, 71, ____

• Triangle G: 121, ___, ___; Triangle H: 70, ___, ___

### Solution

For access, consult one of our IM Certified Partners.

### Problem 2

1. Draw two equilateral triangles that are not congruent.

2. Measure the side lengths and angles of your triangles. Are the two triangles similar?
3. Do you think two equilateral triangles will be similar always, sometimes, or never? Explain your reasoning.

### Solution

For access, consult one of our IM Certified Partners.

### Problem 3

In the figure, line $$BC$$ is parallel to line $$DE$$.

Explain why $$\triangle ABC$$ is similar to $$\triangle ADE$$.

### Solution

For access, consult one of our IM Certified Partners.

### Problem 4

The quadrilateral $$PQRS$$ in the diagram is a parallelogram. Let $$P’Q’R’S’$$ be the image of $$PQRS$$ after applying a dilation centered at a point O (not shown) with scale factor 3.

Which of the following is true?

A:

$$P’Q’= PQ$$

B:

$$P’Q’=3PQ$$

C:

$$PQ=3P’Q’$$

D:

Cannot be determined from the information given

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 2, Lesson 4.)

### Problem 5

Describe a sequence of transformations for which Quadrilateral P is the image of Quadrilateral Q.

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 1, Lesson 6.)