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**4.6 Congruence in Right Triangles**

To Prove Triangles Congruent using the Hypotenuse Leg Theorem

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Right Triangles… In a Right Triangle the side opposite the Right Angle is called the Hypotenuse. The Hypotenuse is always the largest side of the Right Triangle The other two sides are called the Legs. The Legs will always include the Right Angle.

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Side Side Angle? Remember SSA is not a Congruence Rule in All Triangles. It does work however in a special case, Right Triangles. It occurs when hypotenuses and one pair of legs are congruent.

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The HL Theorem!

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So… To Use the HL Theorem, you must show that three conditions are met: There are two right triangles. (Right Angles) The triangles have congruent hypotenuses. There is one pair of congruent legs.

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Example 1B What two triangles are congruent by the Hypotenuse Leg (HL) Theorem? Write a Congruence Statement… ∆LMN ≅ ∆OQP

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**Example 2: Using HL Theorem**

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**Example 3: Using HL Theorem**

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**Closure… How are SAS and HL Theorem alike? How are they Different?**

How does AAS Relate to HL Theorem? (Think Isosceles Triangles…)

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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,

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,

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