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9-12 Integrated Math 2 Unit 2 Lesson 14

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K-5 Math 6-8 Math •9-12 Math

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Integrated Math 1 •Integrated Math 2 Integrated Math 3

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 •Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18

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Unit 2, Lesson 14

Practice with Proportional Relationships

$Course Icon$

Integrated Math 2

Practice

Problem 1

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

\(\frac{A’B’}{AB}=\frac{A’C’}{AC}\)
\(\frac{AD}{A’D’}=\frac{BC}{B’C’}\)
\(\frac{BD}{B’D’}=\frac{C’D’}{CD}\)
\(\frac{AB}{CD}=\frac{A’B’}{C’D’}\)
\(\frac{BC}{A’D’}=\frac{B’C’}{AD}\)

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 2, B C is 3 and D E is 4.

Problem 3

The quilt is made of squares with diagonals. Side length \(AB\) is 2.

What is the length of \(BD\)?
What is the area of triangle \(AEH\)?

<p>Square A B C D.</p>

Problem 4

ForLesson 11: Splitting Triangle Sides with Dilation (Part 2)

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

<p>Triangle A B C.</p> — $\overline{AB} \parallel \overline{A'B'}$

3.5
4
10
10.5

Problem 5

ForLesson 11: Splitting Triangle Sides with Dilation (Part 2)

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.

<p>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.</p>

Problem 6

ForLesson 10: Other Conditions for Triangle Similarity

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

Problem 7

ForLesson 4: Dilating Lines and Angles

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

<p>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.<br>
</p>