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Same Side Interior and Same Side Exterior Angles - Concept

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

When two parallel lines are intersected by a transversal, same side interior (between the parallel lines) and same side exterior (outside the parallel lines) angles are formed. Since alternate interior and alternate exterior angles are congruent and since linear pairs of angles are supplementary, same side angles are supplementary.

If we apply what we know about Alternate Interior and Alternate Exterior angles, then we come up with some interesting things about same side angles. Now what do I mean about same side? Well same side Interior angles would be 4 and 5, so notice we have parallel lines and the transversal. 4 and 5 are on the same side of that transversal.
So if two parallel lines are intersected by a transversal then same side, I'll say interior since this is in between angles are supplementary. But why do they have to be supplementary? Well if we look at what we know about alternate exterior, alternate interior angles we know they have to be congruent. And we know that 5 and 6 here have to be supplementary since they are a linear pair. Which means that 5+6 must be 180 degrees and since 6 and 4 are congruent then by the transitive property which means if 5 and 6 are supplementary then 5 and 4 are supplementary we can say that same side interior angles are supplementary.
The same thing applies for same side exterior angles, so I'm going to erase this and write exterior. But what am I talking about same side exterior, well if I erase these marks exterior means outside of the parallel lines. So if I chose angle two the same side exterior would not be 6 cause 6 is in between the parallel lines but it will be 7. So angle 2 and angle 7 are also supplementary same thing with angle 1 and angle 8. These two are on the same side and will be supplementary.

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