3-2 Proving Lines Parallel Notes
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:
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 (Remind Ms. Vargas to draw a diagram!)
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