Proof: Greater Angle is Subtended by Longer Side in a Triangle

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Издатель Aug 1, 2021

If one angle of a triangle is greater than another, then the side opposite the greater angle is longer than the side opposite the lesser angle. We prove this result in today's geometry video lesson. Note how this is a sort of extension of the converse of the isosceles triangle theorem, which tells us about sides opposite congruent angles, now we are addressing sides opposite non-congruent angles. The converse of this statement is true as well - that is: if a side is greater than another in a triangle, then the angle opposite the longer side is greater than the angle opposite the shorter side. Try proving it yourself, then check out my lesson proving it: https://youtu.be/5Ldq2yigaNU #Geometry

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

Isosceles Triangle Theorem: https://www.youtube.com/watch?v=2GeqKVqwPfc
Exterior Angle Theorem: (coming soon)
Lesson on Exterior Angles Angles in general: https://youtu.be/5M17WkAs0SI

Geometry playlist: https://www.youtube.com/playlist?list=PLztBpqftvzxW-Vql8or1KcngboCBqlr7r

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