Transcript Slide 1
Lesson 3-2: Proving Lines Parallel Teacher: Ms. Olifer What are we learning? SWBAT: use a transversal and prove lines are parallel. Proving Lines Parallel l m 1 2 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. l || m OR: If corresponding angles are congruent, then the lines are parallel. Proving Lines Parallel We know these two lines are parallel!! If Alternate Interior Angles are congruent we can assume lines are parallel too! Proving Lines Parallel l m 1 4 2 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. If 1 2, then l || m. OR: If alternate interior angles are congruent, then the lines are parallel. Proof of Theorem 3-5 (C of AIAT) l 3 1 m Given : 2 1 2 Prove : l ||m Statements 1. Reasons 2 1 1. 2. 2. Vertical's are 2 3 4. l || m 3. 3. 4. Proving Lines Parallel We know these two lines are parallel!! If Same-Side Interior Angles are supplementary, we can assume lines are parallel too!! Proving Lines Parallel l m 1 4 2 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. If 2 and 4 are supplementary, t henl || m. OR: If same side interior angles add up to 180 degrees, then the lines are parallel. Proving Lines Parallel We know these two lines are parallel!! If Alternate Exterior Angles are congruent, we can assume lines are parallel!!! Proving Lines Parallel a 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. If 1 2, t hena || b. OR: If alternate exterior angles are congruent, then the lines are parallel. Proof of Theorem 3-7 (C of AEAT) a 1 4 Given : 2 1 b Prove : a ||b Statements 2 Reasons 1. 1. 14 3. 2 4 2. a || b 4. 2. 4. 3. Proving Lines Parallel We know these two lines are parallel!! If Same-Side Exterior Angles are supplementary, we can assume lines are parallel!!! Proving Lines Parallel a 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. If 1 and 3 are supplementary, then a ||b. 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 m 40° (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