Prove that in an isosceles triangle with an apex angle of 50 degrees, the side is not equal to the base.

In an isosceles triangle, the angles at the base are equal. The angles of a triangle add up to 180 °.
Accordingly, the remaining two angles = (180-50): 2 = 65 °
In the triangle, opposite the larger angle, the larger side lies. Conversely, there is a larger angle opposite the larger side.
Since the angles at the base are greater than the angle at the apex, and the sides lie opposite them, then, accordingly, they will be larger than the base.