# Lesson 9

Conditions for Triangle Similarity

### Problem 1

What is the length of segment $$DF$$?

### Solution

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### Problem 2

In triangle $$ABC$$, angle $$A$$ is 35º and angle $$B$$ is 20º. Select all triangles which are similar to triangle $$ABC$$.

A:

triangle $$DEF$$ where angle $$D$$ is 35º and angle $$E$$ is 20º

B:

triangle $$GHI$$ where angle $$G$$ is 35º and angle $$I$$ is 30º

C:

triangle $$JKL$$ where angle $$J$$ is 35º and angle $$L$$ is 125º

D:

triangle $$MNO$$ where angle $$N$$ is 20º and angle $$O$$ is 125º

E:

triangle $$PQR$$ where angle $$Q$$ is 20º and angle $$R$$ is 30º

### Solution

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### Problem 3

Decide whether triangles $$ABC$$ and $$DEC$$ are similar. Explain or show your reasoning.

### Solution

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### Problem 4

Lin is trying to convince Andre that all circles are similar. Help her write a valid justification for why all circles are similar.

### Solution

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(From Unit 3, Lesson 8.)

### Problem 5

Must these parallelograms be similar? Explain your reasoning.

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### Solution

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(From Unit 3, Lesson 8.)

### Problem 6

Determine if each statement must be true, could possibly be true, or definitely can't be true. Explain or show your reasoning.

1. An equilateral triangle and a right triangle are similar.
2. A right triangle and an isosceles triangle are similar.

### Solution

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(From Unit 3, Lesson 7.)

### Problem 7

Quadrilaterals $$Q$$ and $$P$$ are similar.

What is the scale factor of the dilation that takes $$P$$ to $$Q$$?

A:

$$\frac35$$

B:

$$\frac45$$

C:

$$\frac54$$

D:

$$\frac53$$

### Solution

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(From Unit 3, Lesson 6.)

### Problem 8

The circle centered at $$Q$$ is a scaled copy of the circle centered at $$R$$

1. Find the scale factor.
2. Find the value of $$x$$.

### Solution

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(From Unit 3, Lesson 1.)