1. Lesson 2: (3.2) Proving Lines Parallel

2. What are we learning? Students will… To use a transversal and prove lines are parallel. Evidence Outcome: Prove geometric theorems (lines, angles, triangles, parallelograms). Purpose (Relevancy): To show how to paint parallel lines on a parking lot.

3. Proving Lines Parallel 1l m 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. Limon Language: If corresponding angles are congruent, then the lines are parallel.

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

5. Proving Lines Parallel 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. Limon Language: If alternate interior angles are congruent, then the lines are parallel. l m 14 2

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

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

8. Proving Lines Parallel 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. Limon Language: If same side interior angles add up to 180 degrees, then the lines are parallel. l m 14 2

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

10. Proving Lines Parallel 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. Limon Language: If alternate exterior angles are congruent, then the lines are parallel. a b 1 32

11. Proof of Theorem 3-7 (C of AEAT) 1 2 a b 4 StatementsReasons 1. 2. 3. 4. 1. 2. 3. 4.

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

13. Proving Lines Parallel 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. Limon Language: If same-side exterior angles add up to 180 degrees, then the lines are parallel. a b 1 32

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

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

16. (3.2): Proving Lines Parallel My momma always said, “Life was like a box of chocolates. You never know what you’re gonna get.” -Forrest Homework: (3.2) Pg. 137-139; 1-8 all, 14-22 all, 24-30 even