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.
Proofs
Proof 1
By the Law of Sines, we have . We know , so . Then either or , but the second case would imply , so .
Proof 2
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 .
Proof 3
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 . This article is a stub. Help us out by expanding it.