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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

3. Proving Lines Parallel

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Exercise 14 Page 161

Use the Converse of the Alternate Interior Angles Theorem.

x=50

Practice makes perfect

Both of the given angles are on the inner part of the potential parallel lines, and are on opposite sides of the transversal. Therefore, the angles can be classified as alternate interior angles. According to the Converse of the Alternate Interior Angles Theorem, if the angles are congruent, the lines are parallel.

If these angles are congruent, then the lines will be parallel. Recall that two congruent angles have the same measure. 2x-5 = 95 Let's solve this equation for x.

2x-5 = 95

LHS+5=RHS+5

2x=100

.LHS /2.=.RHS /2.

x = 50

The angles are congruent for x=50. Therefore, for this value of x, we have that l ∥ m.

Subchapter links

Lesson Check p.160

Practice and Problem-Solving Exercises p.160-162

Standardized Test Prep p.163

Mixed Review p.163