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Triangle Congruence by ASA and AAS 4-3

Triangle Congruence by ASA and AAS 4-3. Objective: To prove two triangles congruent using the ASA Postulate and the AAS Theorem. What works and what doesn’t?. Side-Angle-Side ( SAS ). Side-Side-Side ( SSS ). YES. YES. Angle-Side-Angle ( ASA ) . Side-Angle-Angle ( SAA ).

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Triangle Congruence by ASA and AAS 4-3

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  1. Triangle Congruence by ASA and AAS4-3 Objective: To prove two triangles congruent using the ASA Postulate and the AAS Theorem.

  2. What works and what doesn’t? Side-Angle-Side (SAS) Side-Side-Side (SSS) YES YES Angle-Side-Angle (ASA) Side-Angle-Angle (SAA) Side-Side-Angle (SSA) Angle-Angle-Angle (AAA) NO

  3. Angle-Angle-Angle (AAA) Is this statement true? ∆MNO ∆PQR

  4. Which two triangles are congruent by ASA? Explain. We already have pairs of angles. We have congruent sides but are they included? Do congruent sides have congruence markings (ticks)? Yes! To use ASA, we need two pairs of congruent angles and a pair of included congruent sides.

  5. Statement Reason Side-Angle-Angle (AAS) Given Deductive Reasoning B Given Given Third angle Conjecture C A Y ∆ABC ∆XYZ AAS Conjecture (and ASA) Z X

  6. 4-3 p.238: 1-4, 6, 10, 12, 13, 15-18 [Write entire proof in two columns] What works and what doesn’t? Side-Angle-Side (SAS) Side-Side-Side (SSS) YES YES Angle-Side-Angle (ASA) Side-Angle-Angle (SAA) YES YES Side-Side-Angle (SSA) Angle-Angle-Angle (AAA) NO NO

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