Question

9. Given: I II m, m28 = m10
Prove: p ll q

Answer 1

see proof below

Explanation:

You want to show p║q, given ℓ║m and ∠8≅∠10.

Proof

1. ℓ║m and ∠8≅∠10 . . . . given

2. ∠10≅∠2 . . . . corresponding angles are congruent

3. ∠2≅∠8 . . . . transitive property of congruence

4. p║q . . . . converse of alternate interior angles theorem

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Additional comment

Angles 2 and 8 are alternate interior angles where transversal ℓ crosses lines p and q. The Alternate Interior Angles theorem tells you that such angles are congruent if the lines are parallel. Its converse tells you the lines are parallel if such angles are congruent.

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