Triangle Congruence Theorems and Proofs

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Explore the triangle congruence theorems ASA, AAS, and AAS postulates, along with angle-angle-side and side-angle-side rules. Learn how to identify congruent triangles and write two-column proofs. Dive into geometry concepts with visual aids.

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Uploaded on Apr 23, 2025 | 0 Views

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4.3 TRIANGLE 4.3 TRIANGLE CONGRUENCE BY CONGRUENCE BY ASA & & AAS AAS GEOMETRY GEOMETRY ASA

Angle Angle- -Side If 2 angles and the included side of one triangle If 2 angles and the included side of one triangle are congruent to the 2 angles and the included are congruent to the 2 angles and the included side of another triangle, then the 2 triangles are side of another triangle, then the 2 triangles are congruent congruent ??? ??? Side- -Angle (ASA) Postulate Angle (ASA) Postulate

Ex. 1) Ex. 1) Name 2 triangles that are congruent by ASA. Name 2 triangles that are congruent by ASA.

EX. 2) EX. 2) Given: Given: Prove: Prove: ??? ??? ? ? & ?? ?? A Y P X B

EX. 3) EX. 3)

Angle Angle- -Angle Angle- -Side (AAS) Postulate Side (AAS) Postulate If 2 angles and a non If 2 angles and a non- -included side of one triangle included side of one triangle are congruent to 2 angles and a non are congruent to 2 angles and a non- -included side of another triangle, then the 2 triangles are congruent another triangle, then the 2 triangles are congruent included side of ??? ???