How do you find the missing side of a congruent triangle?

Proportions would be the best way; given the sides of the triangle, use ratiOS to find the corresponding side on the congruent triangle.

For example: if three sides are given, 3, 4, and 5, and you had to solve a triangle with lengths 9, 12, and x, this is how you would do it.

Given the triangles are congruent, 4/5 = 12/x

4x = 60

x = 15