4.6 Congruence in Right Triangles To Prove Triangles Congruent using the Hypotenuse Leg Theorem

Right Triangles… 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.

Examples: Tell whether the segment is a leg or a hypotenuse.

Hypotenuse- Leg (HL) Congruence Theorem: If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent. Example: A X B C Y Z

The HL Theorem!

Examples: Determine if the triangles are congruent Examples: Determine if the triangles are congruent. State the postulate or theorem.

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.

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

Example 2: Using HL Theorem

Example 3: Using HL Theorem

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