# Lesson 13

Using the Pythagorean Theorem and Similarity

• Let’s explore right triangles with altitudes drawn to the hypotenuse.

### Problem 1

In right triangle $$ABC$$, altitude $$CD$$ is drawn to its hypotenuse. Select all triangles which must be similar to triangle $$ABC$$.

A:

$$ABC$$

B:

$$ACD$$

C:

$$BCD$$

D:

$$BDC$$

E:

$$CAD$$

F:

$$CBD$$

### Problem 2

In right triangle $$ABC$$, altitude $$CD$$ with length $$h$$ is drawn to its hypotenuse. We also know $$AD=12$$ and $$DB=3$$. What is the value of $$h$$?

### Problem 3

In triangle $$ABC$$ (not a right triangle), altitude $$CD$$ is drawn to side $$AB$$. The length of $$AB$$ is $$c$$. Which of the following statements must be true?

A:

The measure of angle $$ACB$$ is the same measure as angle $$B$$.

B:

$$b^2=c^2+a^2$$.

C:

Triangle $$ADC$$ is similar to triangle $$ACB$$.

D:

The area of triangle $$ABC$$ equals $$\frac{1}{2}h\boldcdot c$$.

### Problem 4

Quadrilateral $$ABCD$$ is similar to quadrilateral $$A’B’C’D’$$. Write 2 equations that could be used to solve for missing lengths.

(From Unit 3, Lesson 12.)

### Problem 5

Segment $$A’B’$$ is parallel to segment $$AB$$.

1. What is the length of segment $$A'A$$?
2. What is the length of segment $$B’B$$?
(From Unit 3, Lesson 11.)

### Problem 6

Lines $$BC$$ and $$DE$$ are both vertical. What is the length of $$AD$$?

A:

4.5

B:

5

C:

7.5

D:

10

(From Unit 3, Lesson 12.)

### Problem 7

Triangle $$DEF$$ is formed by connecting the midpoints of the sides of triangle $$ABC$$. Select all true statements.

A:

Triangle $$BDE$$ is congruent to triangle $$EFC$$

B:

Triangle $$BDE$$ is congruent to triangle $$DAF$$

C:

$$BD$$ is congruent to $$FE$$

D:

The length of $$BC$$ is 8

E:

The length of $$BC$$ is 6

(From Unit 3, Lesson 5.)