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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 12 Page 319

What is the relation between angles ∠ 3 and ∠ 6?

Parallel Lines: u ∥ v
Theorem: Converse of the Consecutive Interior Angles Theorem

Practice makes perfect

Let's begin by highlighting ∠ 3 and ∠ 6 in the diagram.

We can see that ∠ 3 and ∠ 6 are consecutive interior angles of lines u and v. Additionally, we are told that the sum of m∠ 3 and m∠ 6 is 180. m∠ 3+m∠ 6=180 This means that ∠ 3 and ∠ 6 are supplementary angles. Therefore, by the Converse of the Consecutive Interior Angles Theorem we get that u ∥ v.

Subchapter links

Exercises p.318-322