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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. hypotenuse leg leg

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**Hypotenuse-Leg (HL) Congruence Postulate *Only for RIGHT Triangles***

B 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 C A S T R

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**Decide whether the congruence statement is true. **

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

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**Decide whether the congruence statement is true. **

EXAMPLE 2 Use HL Decide whether the congruence statement is true. Explain your reasoning. A C B D SOLUTION It’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.

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

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**Decide whether the congruence statement is true. **

EXAMPLE 4 Use HL Decide whether the congruence statement is true. Explain your reasoning. C D F A B E

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**State the third congruence that must be given to prove that **

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

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Hypotenuse – Leg Congruence Theorem: HL

Hypotenuse – Leg Congruence Theorem: HL

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