Proving Lines Parallel Lesson 3-2: Proving Lines Parallel Teacher: Ms. Olifer

use a transversal and prove lines are parallel. What are we learning? SWBAT: use a transversal and prove lines are parallel.

Proving Lines Parallel 1 2 m Postulate 3-2: Converse (Opposite) of Corresponding Angles Postulate: If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel. OR: If corresponding angles are congruent, then the lines are parallel.

Proving Lines Parallel 72° We know these two lines are parallel!! 72° 108° 72° If Alternate Interior Angles are congruent we can assume lines are parallel too!

Proving Lines Parallel 1 4 2 m Theorem 3-5: Converse of Alternate Interior Angles Theorem If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. OR: If alternate interior angles are congruent, then the lines are parallel.

Proof of Theorem 3-5 (C of AIAT) l 3 1 m 2 Statements Reasons 1. 2. 3. 4.

Proving Lines Parallel 72° We know these two lines are parallel!! 72° 108° 72° If Same-Side Interior Angles are supplementary, we can assume lines are parallel too!!

Proving Lines Parallel 1 4 2 m Theorem 3-6: Converse of Same-Side Interior Angles Theorem If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel. OR: If same side interior angles add up to 180 degrees, then the lines are parallel.

Proving Lines Parallel 108° 72° We know these two lines are parallel!! 72° 108° 72° 108° If Alternate Exterior Angles are congruent, we can assume lines are parallel!!!

Proving Lines Parallel 1 b 3 2 Theorem 3-7: Converse of Alternate Exterior Angles Theorem If two lines and a transversal intersects form alternate exterior angles that are congruent, then the two lines are parallel. OR: If alternate exterior angles are congruent, then the lines are parallel.

Proof of Theorem 3-7 (C of AEAT) 1 4 b 2 Statements Reasons 1. 2. 3. 4.

Proving Lines Parallel 108° 72° We know these two lines are parallel!! 72° 108° 72° 108° If Same-Side Exterior Angles are supplementary, we can assume lines are parallel!!!

Proving Lines Parallel 1 b 3 2 Theorem 3-8: Converse of Same-Side Exterior Angles Theorem If two lines and a transversal intersects form same-side exterior angles that are supplementary, then the two lines are parallel. OR: If same-side exterior angles add up to 180 degrees, then the lines are parallel.

Let’s Apply What We Have Learned…. Find the value of x for which l || m l 40° m (2x + 6)°

You Try One! Find the value of x for which a || b a (7x - 8)° b 62°

Homework… My momma always said, “Life was like a box of chocolates. You never know what you’re gonna get.” -Forrest