Proof: Greater Angle is Opposite the Longer Side in a Triangle | Geometry

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If one side of a triangle is longer than another, then the angle opposite the longer side is greater than the angle opposite the shorter side. We prove this result in today's geometry video lesson. Note how this is a sort of extension of the isosceles triangle theorem, which tells us about angles opposite congruent sides, now we are addressing angles opposite non-congruent sides. The converse of this statement is true as well - that is: if an angle is greater than another in a triangle, then the side opposite the greater angle is longer than the side opposite the lesser angle. Try proving it yourself! #Geometry

Note this is Proposition 18 of Euclid's elements, the converse of Proposition 19.

Proof that the Longer Side is Opposite the Greater Angle: coming soon

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Very nice! I also like that you mentioned AP can be constructed equal to AC because AB is longer. ProofWiki doesn't mention this, but I think it's a nice addition to the proof. By the way, I have a list of all the titles of your videos, and searching "exterior" only returned "What is an Exterior Angle?" which you've already linked to. Thus, I'm pretty sure you don't have a video on the exterior angle theorem.

mike_the_tutor
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Thank you much! I hope you are fine.
These videos are cool. Thanks so much!

aashsyed