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Let’s assume that we have a triangle ABC, where angle A = angle B. We want to prove that side AC = side BC.

To prove this, we will use the Law of Sines. According to the Law of Sines, in any triangle ABC, the ratio of the length of a side to the sine of its opposite angle is constant. Mathematically, it can be written as:

a/sin(A) = b/sin(B) = c/sin(C)

In our case, since angle A = angle B, we can rewrite the equation as:

a/sin(A) = b/sin(A)

Cross-multiplying, we get:

a * sin(A) = b * sin(A)

Dividing both sides by sin(A), we get:

a = b

Therefore, we have proved that if two angles of a triangle are equal, then the sides opposite those angles are also equal.