Understanding Congruent Right Triangles: Hypotenuse-Leg Theorem

DESCRIPTION

In this chapter, we explore the concept of congruence in right triangles, focusing on Theorem 4-6, known as the Hypotenuse-Leg (HL) Theorem. This theorem states that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent. We will provide proofs and examples to illustrate the application of the HL Theorem in proving triangle congruence. Additional exercises are included for practice.

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Mar 18, 2014

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Understanding Congruent Right Triangles: Hypotenuse-Leg Theorem

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Chapter 4: Congruent Triangles 4.6 Congruence in Right Triangles
Right Triangles
Theorem 4-6 • Hypotenuse-Leg (HL) Theorem • If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
Proof of the HL Theorem • Given: ΔPQR & ΔXYZ are right triangles • Prove:
Example 2 • Given: AD is the perpendicular bisector of CE • Prove:
Example 3 • Given: W & K are right angles • Prove:
Example 3a • Given: PRS & RPQ are right angles • Prove:
Example 4 • Given: LO bisects angle MLN • Prove:
Homework • p. 237 • 3, 4, 6-8, 10, 11, 13, 14