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Transcript
Triangle Congruence Shortcuts Guided Notes Instead of having to check all corresponding sides and all corresponding angles being congruent, for triangles we can use these shortcuts to only check three Theorems Theorem Postulate 4-1 Side-Side-Side (SSS) Postulate Postulate 4-2 Side-Angle-Side (SAS) Postulate If… 3 sides of one triangle are congruent to 3 sides of another, 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, Then… the two triangles are congruent. Theorems Theorem Postulate 4-3Angle-Side-Angle (ASA) Postulate If… 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another, Then… the two triangles are congruent. Theorem 4-2 Angle-Angle-Side (AAS/SAA) Theorem 2 angles and a nonincluded side of one triangle are congruent to 2 angles and a nonincluded side of another, Theorem Theorem 4-6Hypotenuse-Leg (HL) Theorem If… the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, WORK DON’T WORK Then… the two triangles are congruent. EXAMPLES Name the congruence postulate that allows you to conclude: S D Y Z A C R P X B a. ∆ABC≅∆ADC b. ∆PRS≅∆XYZ Z C D W A B S P c. ∆ABC≅∆DCB Homework: Sec 4.2-3-6 WS O N R Y X M d. ∆WXY≅∆WZY e. ∆PRS≅∆ONM