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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Parallel Lines and Proportional Parts

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Exercise 53 Page 581

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

8

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. We can use the Triangle Proportionality Theorem.

The lengths of the segments intercepted by the parallel line are proportional. Since the two marked segments are congruent and 3x+2=4x-6, we can solve this equation to find x.

3x+2=4x-6

▼

Solve for x

LHS+6=RHS+6

3x+8=4x

LHS-3x=RHS-3x

8=x

Rearrange equation

x=8

We found that x=8.

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Exercises p.577-581