Congruence in Right Triangles and HL Theorem
In right triangles, Side-Side-Angle is not valid for congruence, except in the special case of right triangles where the right angles are the nonincluded angles. The Hypotenuse-Leg (HL) Theorem states that 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. This concept is illustrated with examples and conditions necessary for applying the HL Theorem.
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Presentation Transcript
4-6 Congruence in Right Triangles
Notice the triangles are not congruent, so we can conclude that Side-Side-Angle is NOT valid. However Side-Side-Angle, works in the special case of right triangles, where the right angles are the nonincluded angles.
Hypotenuse: The side opposite the right angles Legs: the other two sides of the triangle
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
Conditions for HL Theorem To use the HL Theorem, the triangles must meet these three conditions: There are two right triangles The triangles have congruent hypotenuses There is one pair of congruent legs
