# Lesson 14

Side Length Quotients in Similar Triangles

Let’s find missing side lengths in triangles.

### Problem 1

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

### 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 $$ABC$$.

### Problem 3

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

### 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.

(From Unit 2, Lesson 10.)

### Problem 5

Which is a scaled copy of Polygon A? Identify a pair of corresponding sides and a pair of corresponding angles. Compare the areas of the scaled copies.

(From Unit 2, Lesson 2.)

### Problem 6

A map of Colorado says that the scale is 1 inch to 20 miles or 1 to 1,267,200. Are these two ways of reporting the scale the same? Explain your reasoning.

(From Unit 2, Lesson 7.)