If two triangles are are congruent to one another and they are both isosceles, then they will have equivalent side lengths and congruent base angles. Slices of pizza are a prime example of congruent isosceles triangles. In the diagram above, the two missing slices were congruent by the AAA Theorem.
The two base sides are tangent to the circle. They are also opposite each other causing them to be parallel. The two pairs of base angles are congruent based upon the alternate interior angles theorem. The two non-base angles are congruent based upon the vertical angles congruence theorem. Based of these geometric ideas, slices of pizza are congruent triangles. By definition, isosceles triangles have two congruent sides. In this case, the pizza was cut into isosceles triangles, however it could have been cut into equilateral triangles (these are still isosceles). In the real world, when people order a pizza, they want it cut so that each will get the same amount. By cutting a pizza into congruent triangles, this is assured.
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