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3-2 Proving Lines Parallel Warm Up-Find the value of x and the angle measures. Justify your answer with a theorem or postulate. • 1. • 2. Postulate 3-2: Converse of the Corresponding Angles Postulate • If 2 lines and a transversal form corresponding angles that are congruent, then the two lines are parallel. Flow Proofs • A flow proof is a more graphic type of proof • It uses arrows to show the connections of logic used to get to the proof • Format: ∡1 ≅ ∡2 Given Another expression A reason 𝐴𝑛𝑜𝑡ℎ𝑒𝑟 𝐸𝑥𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛 Another reason 𝐶𝑜𝑛𝑐𝑙𝑢𝑠𝑖𝑜𝑛 Another reason Creating a Flow Proof Theorem 3-5 Converse of the Alternate Interior Angles Theorem • If 2 lines and a transversal for alternate interior angles that are congruent, then the 2 lines are parallel Prove: • If ∡3 ≅ ∡6, then 𝑙 ∥ 𝑚 Theorem 3-6 Converse of Same-Side Interior Angles theorem • If 2 lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel Prove: • If ∡4 𝑎𝑛𝑑 ∡6 are supplementary, then 𝑙 ∥ 𝑚 Using Theorems 3-5 and 3-6 • Which lines, if any, must be parallel if ∡1 ≅ ∡2 ? Justify your answer using a theorem or postulate. More Theorems • Theorem 3-7: Converse of the Alternate Exterior Angles Theorem • If 2 lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel • If ∡1 ≅ ∡8, 𝑡ℎ𝑒𝑛 𝐶𝐷 ∥ 𝐸𝐹 • Theorem 3-8: Converse of the Same-Side Exterior Angle Theorem • If 2 lines and a transversal form same-side exterior angles that are supplementary, then the two lines are parallel • If ∡1 ≅ ∡7, 𝑡ℎ𝑒𝑛 𝐶𝐷 ∥ 𝐸𝐹 Proof: Theorem 3-8 • Given : ∡1 ≅ ∡7 • Prove: 𝐶𝐷 ∥ 𝐸𝐹 Using Algebra • Find the value of x for which 𝑙 ∥ 𝑚 Homework • Create a flow proof for theorem 3-7 • Create a two-column proof for theorem 3-8 • Do #2, 4, 6, and 8 on pg. 137 in textbook