Base Angle 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
.
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