# Lesson 9

Side Length Quotients in Similar Triangles

### Problem 1

These two triangles are similar. What are $$a$$ and $$b$$? Note: the two figures are not drawn to scale. ### Solution

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### Problem 2

Here is triangle $$ABC$$. Triangle $$XYZ$$ is similar to $$ABC$$ with scale factor $$\frac 1 4$$. 1. Draw what triangle $$XYZ$$ might look like.
2. How do the angle measures of triangle $$XYZ$$ compare to triangle $$ABC$$? Explain how you know.

3. What are the side lengths of triangle $$XYZ$$?

4. For triangle $$XYZ$$, calculate (long side) $$\div$$ (medium side), and compare to triangle $$ABC$$.

### Solution

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### Problem 3

The two triangles shown are similar. Find the value of $$\frac d c$$. ### Solution

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### Problem 4

The diagram shows two nested triangles that share a vertex. Find a center and a scale factor for a dilation that would move the larger triangle to the smaller triangle. ### Solution

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(From Unit 2, Lesson 5.)