PROPOSITION XVIII. THEOREM.
DEMONSTRATION.
We wish to prove that
In any isosceles triangle, the angles opposite the equal sides are equal.
Let the triangle A B C be isosceles, having the side A B equal to the side A C; then will the angle B, opposite the side A C, be equal to the angle C, opposite the equal side A B.
For draw the line A D so as to divide the angle A into two equal parts, and let it be long enough to divide the side B C at some point as D.
Now the two triangles A D B, A D C, have the side A B of the one equal to the side A C of the other, the side A D common to both, and the included angle B A D of the one equal to the included angle C A D of the other; therefore the two triangles are equal in all respects, and the angle B, opposite the side A C, is equal to the angle C, opposite the side A B.
