http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines
James Sousa: Proof of Alternate Interior Angles Converse
Guidance
Alternate Interior Anglesare two angles that are on theinterior oflandm, but on opposite sides of the transversal.
(^63) and (^66) are alternate interior angles.
Alternate Interior Angles Theorem:If two parallel lines are cut by a transversal, then the alternate interior angles
are congruent.
Proof of Alternate Interior Angles Theorem:
Given:l||m
Prove:^63 ∼=^66
TABLE3.2:
Statement Reason
1.l||m Given
2.^63 ∼=^67 Corresponding Angles Postulate
3.^67 ∼=^66 Vertical Angles Theorem
4.^63 ∼=^66 Transitive PoC
There are several ways we could have done this proof. For example, Step 2 could have been^62 ∼=^6 6 for the same
reason, followed by^62 ∼=^6 3. We could have also proved that^64 ∼=^6 5.
Converse of Alternate Interior Angles Theorem:If two lines are cut by a transversal and alternate interior angles
are congruent, then the lines are parallel.
Example A
Findm^6 1.