Problem 1 Identifying Parallel Lines

Which lines are parallel if ∠ 1 ≅ ∠ 2 ? angle 1 approximately equal to angle 2 question mark  Justify your answer.

∠ 1 angle 1  and ∠ 2 angle 2  are corresponding angles. If ∠ 1 ≅ ∠ 2 , angle 1 approximately equal to angle 2 comma  then a || b eh vertical linevertical line b  by the Converse of the Corresponding Angles Postulate.

Image Long Description

✓ Got It?

1. Which lines are parallel if ∠ 6 ≅ ∠ 7 ? angle 6 approximately equal to angle 7 question mark  Justify your answer.

Take Note: Theorem 3-4 Converse of the Alternate Interior Angles Theorem

Theorem

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

If …

∠ 4 ≅ ∠ 6 angle 4 approximately equal to angle 6

Then …

l || m l vertical linevertical line m

Theorem 3-5 Converse of the Same-Side Interior Angles Theorem

Theorem

If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel.

If …

m ∠ 3 + m ∠ 6 = 180 m angle , 3 plus , m angle , 6 equals 180

Then …

l || m l vertical linevertical line m

You will prove Theorem 3-5 in Exercise 29.

Theorem 3-6 Converse of the Alternate Exterior Angles Theorem

Theorem

If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel.

If …

∠ 1 ≅ ∠ 7 angle 1 approximately equal to angle 7

Then …

l || m l vertical linevertical line m