# Lesson 15

Finding All the Unknown Values in Triangles

### Problem 1

In the right triangles shown, the measure of angle $$ABC$$ is the same as the measure of angle $$EBD$$.  ​​​What is the length of side $$BE$$?

### Solution

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### Problem 2

In right triangle $$ABC$$, angle $$C$$ is a right angle, $$AB=13$$, and $$BC=5$$. What is the length of $$AC$$?

### Solution

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### Problem 3

In this diagram, lines $$AC$$ and $$DE$$ are parallel, and line $$DC$$ is perpendicular to each of them. What is a reasonable estimate for the length of side $$BE$$?

A:

$$\frac{1}{3}$$

B:

1

C:

$$\frac{5}{3}$$

D:

5

### Solution

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### Problem 4

Select all of the right triangles.

A:

Triangle $$ABC$$ with $$AB = 30$$, $$BC = 40$$, and $$AC = 50$$

B:

Triangle $$XYZ$$ with $$XY = 1$$, $$YZ = 1$$, and $$XZ = 2$$

C:

Triangle $$EFG$$ with $$EF = 8$$, $$FG = 15$$, and $$EG = 17$$

D:

Triangle $$LMN$$ with $$LM = 7$$, $$MN = 24$$, and $$LN = 25$$

E:

Triangle $$QRS$$ with $$QR = 4$$, $$RS = 5$$, and $$QS = 6$$

### Solution

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(From Unit 3, Lesson 14.)

### Problem 5

Andre says he can find the length of the third side of triangle $$ABC$$ and it is 13 units. Mai disagrees and thinks that the side length is unknown. Who do you agree with? Show or explain your reasoning.

### Solution

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(From Unit 3, Lesson 14.)

### Problem 6

In right triangle $$ABC$$, altitude $$CD$$ with length $$h$$ is drawn to its hypotenuse. We also know $$AD=8$$ and $$DB=2$$. What is the value of $$h$$?

### Solution

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(From Unit 3, Lesson 13.)

### Problem 7

Select the sequence of transformations of triangle $$ADE$$ that would show that triangles $$ABC$$ and $$AED$$ are similar. The length of $$AC$$ is 6.

A:

Dilate from center $$A$$ by a scale factor of $$2$$, then reflect over line $$AC$$.

B:

Dilate from center $$A$$ by a scale factor of $$2$$, then rotate 60º around angle $$A$$.

C:

Translate by directed line segment $$DC$$, then reflect over line $$AC$$.

D:

Dilate from center $$A$$ by a scale factor of $$4$$, then reflect over line $$AC$$.

### Solution

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(From Unit 3, Lesson 7.)