Lesson 12

Practice With Proportional Relationships

Problem 1

Quadrilateral $$ABCD$$ is similar to quadrilateral $$A’B’C’D’$$. Select all statements that must be true.

A:

$$\frac{A’B’}{AB}=\frac{A’C’}{AC}$$

B:

$$\frac{AD}{A’D’}=\frac{BC}{B’C’}$$

C:

$$\frac{BD}{B’D’}=\frac{C’D’}{CD}$$

D:

$$\frac{AB}{CD}=\frac{A’B’}{C’D’}$$

E:

$$\frac{BC}{A’D’}=\frac{B’C’}{AD}$$

Solution

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Problem 2

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

Solution

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Problem 3

The quilt is made of squares with diagonals. Side length $$AB$$ is 2.

1. What is the length of $$BD$$?
2. What is the area of triangle $$AEH$$

Solution

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Problem 4

Segment $$A’B’$$ is parallel to segment $$AB$$. What is the length of segment $$BB'$$?

A:

3.5

B:

4

C:

10

D:

10.5

Solution

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(From Unit 3, Lesson 11.)

Problem 5

Elena thinks length $$BC$$ is 16.5 units. Lin thinks the length of $$BC$$ is 17.1 units. Do you agree with either of them? Explain or show your reasoning.

Solution

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(From Unit 3, Lesson 11.)

Problem 6

Mai thinks knowing the measures of 2 sides is enough to show triangle similarity. Do you agree? Explain or show your reasoning.

Solution

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(From Unit 3, Lesson 10.)

Problem 7

Line $$g$$ is dilated with a center of dilation at $$A$$. The image is line $$f$$. Approximate the scale factor.

Solution

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(From Unit 3, Lesson 4.)