AoPSWiki
NEW! Hard Problems DVD
A documentary about the 2006 US IMO team. Features many current and past AoPS members!
Click here for more details and to order
Personal tools

Base Angle Theorem

From AoPSWiki

The Base Angle Theorem states that in an isosceles triangle, the angles opposite the congruent sides are congruent.

Proof

Since the triangle only has three sides, the two congruent sides must be adjacent. Let them meet at vertex .

Now we draw height to . From the Pythagorean Theorem, , and thus is similar to , and . [Asy_image]

Preparing for MATHCOUNTS or the AMC contests, and having a tough time with number theory problems? Read Art of Problem Solving's Introduction to Number Theory by Mathew Crawford.
© Copyright 2008 AoPS Incorporated. All Rights Reserved. • FoundationPrivacyContact Us