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SAS and HL Congruence

SAS and HL Congruence. Section 4.4. 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. BC DA , BC AD. ABC CDA. STATEMENTS. REASONS.

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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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