Download 3-2 Proving Lines Parallel

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