Question 159413
Draw the isosceles triangle. Then draw the altitude. 
That is what you are "given"

You also know that two angles of the isosceles triangle are equal. Let the two equal angles in the original isosceles triangle be A. 

Euclid tells us that every triangle has 180 degrees of interior angle in it.
So the third angle in the isosceles triangle is (180-2A)

By definition, an altitude forms a right angle with the base it intersects.
Thus there are 2 right angles formed at the foot of the altitude.

So, you can now show that the two angles formed at the vertex where the altitude was dropped from must be equal (each being 180-90-A) = 90-A

(90-A) = 1/2(180-2A)
Thus the two new angles are equal, and are 1/2 the size of the original one. So the original angle is bisected by the altitude.