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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) YES Side-Side-Side (SSS) YES Angle-Side-Angle (ASA) Side-Angle-Angle (SAA) Side-Side-Angle (SSA) Angle-Angle-Angle (AAA) (naughty donkey) NO Angle-Angle-Angle (AAA) Is this statement true? ∆MNO ∆PQR 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)? SinceU E, UV EO, andV O, ΔSUV ΔNEO Statement Angle-Angle-Side (AAS) Deductive Reasoning B C A Y BC YZ A X B Y Given C Z Third angle Conjecture ∆ABC ∆XYZ X Z Reason Given Given AAS Conjecture (and ASA) What works and what doesn’t? 4-3 p.238: 1-4, 6, 10, 12, 13, 15-18 Side-Angle-Side (SAS) YES Side-Side-Side (SSS) YES [Write entire proof Angle-Side-Angle (ASA) in two columns] Side-Angle-Angle (SAA) YES Angle-Angle-Angle (AAA) NO YES Side-Side-Angle (SSA) (naughty donkey) NO