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Congruence in Right Triangles. hypotenuse. legs. Right Triangles. The side opposite the right angle is the longest side and is called the hypotenuse . The other two sides are called legs. B. Y. C. Z. A. X. Theorem 4-6 Hypotenuse-Leg (HL) Theorem
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hypotenuse legs Right Triangles • The side opposite the right angle is the longest side and is called the hypotenuse. • The other two sides are called legs.
B Y C Z A X Theorem 4-6 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. ABC XYZ
Why? DGF DEF
What additional information do you need to prove the triangles congruent by HL?
When proving triangles are congruent by HL, the following conditions must be met: • The hypotenuses are congruent. • At least one set of legs is congruent. • You have two right triangles.
C A B D Since BC ≅AD, <ABC and <DBC are right angles. Since <ABC and <DBC are right angles, Then ΔABC and Δ DBC are right triangles.
