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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 25 Page 608

Apply the Corresponding Angles Theorem, then write a proportion using the Triangle Proportionality Theorem.

22.5

Practice makes perfect

Let's analyze the given figure.

Since the two marked right angles are congruent, according to the Corresponding Angles Theorem, the segment in the middle of this triangle is parallel to one of its sides. This means that we can use the Triangle Proportionality Theorem.

The lengths of the segments intercepted by the parallel line are proportional. Let's write a proportion using the lengths of the segments. 8/18=10/x Let's solve it using the Cross Product Property.

8/18=10/x

▼

Solve for x

Cross multiply

8 * x=18 * 10

Multiply

8x=180

.LHS /8.=.RHS /8.

x=180/8

Calculate quotient

x=22.5

We found that x=22.5.

Subchapter links

1 Ratios and Proportions p.607

2 Similar Polygons p.607

3 Similar Triangles p.608

4 Parallel Lines and Proportional Parts p.608

5 Parts of Similar Triangles p.609

6 Similarity Transformations p.609

7 Scale Drawings and Models p.610