Download 3.3 Prove Lines are Parallel

Geometry Chapter 3: Parallel and Perpendicular Lines 3.3-­‐ Prove Lines are Parallel SWBAT: use angles relationships to prove lines are parallel. Common Core: G.CO.12
“Do Now”
Find the values of 𝒙 & 𝒚.
Postulate 16: Corresponding Angles Converse If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are _________________________________. Example 1: Find the value of 𝑥 that makes 𝑚 ∥ 𝑛. Geometry Chapter 3: Parallel and Perpendicular Lines Example: Find the value of 𝑦 that makes 𝑎 ∥ 𝑏. Theorem 3.4: Alternate Interior Angles Converse If two lines are cut by a transversal so that the alternate interior angles are congruent, then the lines are ______________________________. Theorem 3.5: Alternate Exterior Angles Converse If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are ______________________________. Theorem 3.6: Consecutive Interior Angles Converse If two lines are cut by a transversal so the consecutive interior angles are ____________________________________, then the lines are parallel. Geometry Chapter 3: Parallel and Perpendicular Lines Example: Prove that if two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel. Given: ∠4 ≅ ∠5 Prove: 𝑔 ∥ ℎ Statements Reasons Geometry Chapter 3: Parallel and Perpendicular Lines Example: Given: 𝑟 ∥ 𝑠 and ∠1 ≅ ∠3 Prove: 𝑝 ∥ 𝑞 Theorem 3.7: Transitive Property of Parallel Lines If two lines are parallel to the ______________________________, then they are parallel to each other. Example: The flag of the United States has 13 alternating red and white stripes. Each stripe is parallel to the stripe immediately below it. Explain why the top stripe is parallel to the bottom stripe. Geometry Chapter 3: Parallel and Perpendicular Lines Example: In the figure each rung of the ladder is parallel to the rung directly above it. Explain why the top rung is parallel to the bottom rung. Practice: Homework: Pgs. 165 – 167 #’s 3 -­‐23 Odd, 29, 31