4-6 Congruence in Right Triangles

Objective

To prove right triangles congruent using the Hypotenuse-Leg Theorem

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In the diagram below, two sides and a nonincluded angle of one triangle are congruent to two sides and the nonincluded angle of another triangle.

Notice that the triangles are not congruent. So, you can conclude that Side-Side-Angle is not a valid method for proving two triangles congruent. This method, however, works in the special case of right triangles, where the right angles are the nonincluded angles.

In a right triangle, the side opposite the right angle is called the hypotenuse. It is the longest side in the triangle. The other two sides are called legs.

Essential Understanding You can prove that two triangles are congruent without having to show that all corresponding parts are congruent. In this lesson, you will prove right triangles congruent by using one pair of right angles, a pair of hypotenuses, and a pair of legs.

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