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This lesson focuses on the Hypotenuse-Leg (HL) Congruence Theorem, which states that if the hypotenuse and one leg of a right triangle are congruent to the corresponding parts of another right triangle, then the two triangles are congruent. Students will learn the names of the sides of right triangles, identify legs and hypotenuses, and determine congruence using various postulates such as SSS, SAS, AAS, ASA, and specifically HL. Examples will illustrate these concepts in practice.
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5.4 Hypotenuse-Leg (HL) Congruence Theorem Objective: To use the HL Congruence Theorem and summarize congruence postulates and theorems.
Side Names of Triangles • Right Triangles: side across from right angle is the hypotenuse, the remaining two are legs. leg hypotenuse leg
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: because of HL. A X B C Y Z
Examples: Determine if the triangles are congruent. State the postulate or theorem.
Triangles are congruent when you have… SSS AAS SAS ASA HL
