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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. Proving Lines Parallel

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Exercise 11 Page 319

What is the relation between angles ∠ 7 and ∠ 8?

Parallel Lines: r ∥ s
Theorem: Converse of the Consecutive Interior Angles Theorem

Practice makes perfect

Let's begin by highlighting ∠ 7 and ∠ 8 in the diagram.

We can see that ∠ 7 and ∠ 8 are consecutive interior angles of lines r and s. Additionally, we are told that the sum of m∠ 7 and m∠ 8 is 180. m∠ 7+m∠ 8=180 This means that ∠ 7 and ∠ 8 are supplementary angles. Therefore, by the Converse of the Consecutive Interior Angles Theorem, we get that r ∥ s.

Subchapter links

Exercises p.318-322