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Lesson 2: (3.2) Proving Lines Parallel

Lesson 2: (3.2) Proving Lines Parallel. What are we learning?. Students will… To use a transversal and prove lines are parallel. Evidence Outcome : Prove geometric theorems (lines, angles, triangles, parallelograms).

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Lesson 2: (3.2) Proving Lines Parallel

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  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 l 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.Limon Language: If corresponding angles are congruent, then the lines are parallel.

  4. 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!

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

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

  7. 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!!

  8. 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. Proving Lines Parallel l 1 4 2 m

  9. 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!!!

  10. 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. Proving Lines Parallel a 1 b 3 2

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

  12. 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!!!

  13. 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.Limon Language: If same-side exterior angles add up to 180 degrees, then the lines are parallel.

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

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

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

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