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In this lesson, we will explore the Hypotenuse-Leg (HL) Theorem, which states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent. We will define key terms such as hypotenuse and leg, and outline the conditions necessary for the HL Theorem to apply. Through examples, we will demonstrate how to apply this theorem to prove the congruence of right triangles and solidify your understanding of triangle congruence.
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4.6 Congruence in Right Triangles Objective: I will prove right triangles congruent using the Hypotenuse-Leg Theorem
Vocab: • Hypotenuse: the side opposite the right angle, or the longest side of a triangle • Legs: two shorter sides of a triangle Leg hypotenuse Right Angle Leg
Theorem 4-6: Hypotenuse-Leg (HL) Theorem If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, the then triangles are congruent If: Then: ABC and DEF are right s and ABC DEF AC DE and CB DF D C A B F E
Key Concept…Conditions for HL Theorem 1. There are 2 right triangles 2. The triangles have congruent hypotenuses 3. There is one pair of congruent legs
