The Alternate Interior Angle Theorem (feat. A. Passey)
Channel: Andrew Misseldine
Date: 2020-04-20

In this video, we see a proof of the Alternate Interior Angle Theorem, that is, in a congruence geometry if two lines are transversed in such a way that alternate interior angles are congruent then the two lines are parallel. One should be cautious though. This does not prove the converse of the Alternate Interior Angle Theorem, that is, if two lines are parallel then all transverals cut the parallel lines in such a way that alternate interior angles are congruent. This converse is actually equivalent to the Euclidean Parallel Postulate and will be discussed later in this lecture series.

This is part 17 (2/3) of the lecture series offered by Dr. Andrew Misseldine for the course Math 3130 - Modern Geometries at Southern Utah University. This lecture video features a guest lecturer, Adam Passey. A transcript of this lecture can be found at Dr. Misseldine's website or through his Google Drive at: 
https://drive.google.com/file/d/1rkl70_QxT23e7MqMObNEQNo4S7u-iYU7/view

This lecture is loosely based upon Section 3.2 of Roads to Geometry by Wallace & West. Please post any questions you might have below in the comment field and Dr. Misseldine (or other commenters) can answer them for you. Please also subscribe for further updates.