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SAS and HL Congruence

This document explains the Side-Angle-Side (SAS) and Hypotenuse-Leg (HL) Congruence Theorems in triangle geometry. The SAS theorem states that if two sides and the included angle of one triangle are congruent to another triangle, the triangles are congruent. The HL theorem asserts that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. The document provides examples and proofs for both theorems.

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SAS and HL Congruence

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  1. SAS and HL Congruence Section 4.4

  2. Side-Angle-Side (SAS) Congruence Theorem • If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

  3. BC DA,BC AD ABCCDA STATEMENTS REASONS S BC DA Given Given BC AD BCADAC A Alternate Interior Angles Theorem S ACCA Reflexive Property of Congruence EXAMPLE 1 Use the SAS Congruence Postulate Write a proof. GIVEN PROVE

  4. Hypotenuse-Leg (HL) Congruence Theorem • If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.

  5. GIVEN WY XZ,WZ ZY, XY ZY WYZXZY PROVE EXAMPLE 3 Write a proof.

  6. STATEMENTS REASONS H WY XZ Given WZ ZY, XY ZY Given Definition of lines Z andY are right angles Definition of a right triangle WYZand XZY are right triangles. ZY YZ L Reflexive Property of Congruence WYZXZY HL Congruence Theorem EXAMPLE 3

  7. Assignment • p. 243: 3-16, 25-27

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