The most difficult mathematics is that which you do not know. A surprising amount of mathematics is actually easy once you've learned it. Of course, once you learn the easy stuff, then you have to start tacking the deep stuff, and that gets harder.
An isosceles triangle has two sides of equal length. An isosceles triangle also has two angles of the same measure; namely, the angles opposite to the two sides of the same length; this fact is the content of the isosceles triangle theorem, which was known by Euclid.
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.