# M15

Question: Determine which of the triangles are congruent to A in the diagram below. State which of the congruence rules you use.

Answer: Let’s check each shape individually.

Shape B: it has two angles in common with A, but the side is a different length.

Shape C: this has two angles and a side-length in common with A, but to pass the ASA test the side-length needs to be between the two angles, which in C’s case it isn’t.

Shape D: this does what shape C didn’t – all the numbers match, and the side we know is between the two angles which means that shape D is congruent to A by the ASA criteria.

The real value in being able to spot when two triangles are congruent like this is that we suddenly know that all the other angles and side-lengths must also be the same.This is useful in making quick leaps towards solving bigger problems, for example in circle theorems, so keep the definition of congruence as well as the 4 tests for congruent triangles in mind when solving all kinds of geometry problems.