7. Congruence in Overlapping Triangles
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If we want to prove that △ACD≅△CAB, the first thing we need to do is to prove that AB≅DC. We can also choose another path as there are multiple ways to solve this exercise.
As we can notice, △ACD and △CAB are right triangles and the hypotenuses and one of their legs are congruent. In this case, we use the Hypotenuse-Leg (HL) Theorem.
Hypotenuse-Leg (HL) Theorem |
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent. |
The illustration of the theorem is given below.