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4.4 – Prove Triangles Congruent by HL Geometry Ms. Rinaldi

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Right Triangles In a right triangle, the sides next to the right angle are called the legs. The side opposite the right angle is called the hypotenuse. leg hypotenuse

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Hypotenuse-Leg (HL) Congruence Postulate *Only for RIGHT Triangles* If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent. If it’s a right triangle, Hypotenuse Leg Then A B C R S T

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EXAMPLE 1 Use HL Decide whether the congruence statement is true. Explain your reasoning. SOLUTIONIt’s a right triangle ( H) (L) So by HL, A B CD

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EXAMPLE 2 Use HL Decide whether the congruence statement is true. Explain your reasoning. SOLUTIONIt’s a not a right triangle, so HL does not apply. Also, you have an Angle-Side- Side, but ASS is not a congruence postulate, so there is not enough information. A B C D

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EXAMPLE 3 Use HL Decide whether the congruence statement is true. Explain your reasoning.

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EXAMPLE 4 Use HL Decide whether the congruence statement is true. Explain your reasoning. AB CD E F

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EXAMPLE 5 Use HL State the third congruence that must be given to prove that using the indicated postulate. A B C D E F Given: Angle A and D are right angles. Use the HL Congruence Postulate.

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