What strategy is used to find the missing value in a congruent triangle?

The strategy of setting up an equivalent proportion is effective for finding a missing value in congruent triangles because congruent triangles have identical corresponding angles and sides. When two triangles are congruent, any side length of one triangle can be expressed as a proportionate side length of the other triangle.

For example, if you know the lengths of some sides of one triangle and need to find a missing side in a congruent triangle, you can set up a proportion comparing the lengths. This allows you to solve for the unknown value using the properties of congruence, which ensures that the ratios of corresponding sides are equal.

This method is particularly useful in problems involving similar triangles as well, where the sides are in proportion, making it a fundamental strategy in solving many geometric problems. Misapplying other methods, such as trial and error or measuring all angles, may not yield accurate results or take more time, whereas using proportion takes advantage of the known relationships that exist in congruent triangles.