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Pearson Geometry Common Core, 2011 View details

3. Proving Lines Parallel

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Exercise 45 Page 162

Use the Converse of the Same-Side Interior Angles Postulate.

PN ∥ LA, see solution

Practice makes perfect

Let's start by recalling the Converse of the Same-Side Interior Angles Postulate.

Converse of the Same-Side Interior Angles Postulate
If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel.

To apply the postulate, let's draw quadrilateral PLAN using the given angles. Let's also extend its sides.

We see that, in this case, the interior angles are supplementary only in the vertical direction, so we can determine only one pair of parallel lines. PN ∥ LA