Lesson 12

Practice With Proportional Relationships

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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 \(AD\)?

Line A B is horizontal and has 3 points, A, B and D. Lines B C and D E are vertical. Line A C goes through C on B C and E on D E. A B is 3, B C is 2 and D E is 5.  

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 \(AEH\)? 
Square A B C D.

Solution

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Problem 4

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

Triangle A B C.
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. 

Triangle A B C has segment D E, with D on A B and E on A C. A D is 4, D B is 2, A E is 9 and E C is 5 and D E is 11.

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.

Parallel lines f and g. Line g is above and to the left of line f. Point C on line F. Point B on line g. Point A above and to the left of line G. Point D below and to the right of line f.  

Solution

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(From Unit 3, Lesson 4.)