Base Angle Theorem
(Redirected from Hinge Theorem)
The Base Angle Theorem states that in an isosceles triangle, the angles opposite the congruent sides are congruent.
Since the triangle only has three sides, the two congruent sides must be adjacent. Let them meet at vertex .
Now we draw altitude to . From the Pythagorean Theorem, , and thus is congruent to , and .
We know that (given). By the reflexive property, we know that . We know that (given). By SSS, we conclude that . By CPCTC, we conclude that .
Even Simpler Proof
By the Law of Sines, we have . We know , so . Then either or , but the second case would imply , so .