Ans: SSS (Side-Side-Side): If three sides of one triangle are equal to the three corresponding sides of another triangle, the triangles are congruent.

Ans: Draw AD ⊥ BC. In △ABD and △ACD: AB = AC (given), AD = AD (common), ∠ADB = ∠ADC = 90°. By RHS, △ABD ≅ △ACD. Therefore ∠B = ∠C (CPCT).

Ans: Let △ABC with AB > AC. We need to show ∠ACB > ∠ABC. Since AB > AC, mark D on AB such that AD = AC. Then △ACD is isosceles, so ∠ACD = ∠ADC. Now ∠ADC is an exterior angle of △BCD, so ∠ADC > ∠DBC = ∠ABC. Therefore ∠ACD > ∠ABC. Since ∠ACB > ∠ACD, we get ∠ACB > ∠ABC.

Ans: Valid: SSS (all three sides equal), SAS (two sides and included angle), ASA (two angles and included side), AAS (two angles and non-included side), RHS (right angle, hypotenuse, one side for right triangles). NOT valid: AAA — same shape but not necessarily same size (similar, not congruent). SSA (or ASS) — two sides and a non-included angle do not uniquely determine a triangle; two different triangles can satisfy the same SSA condition. Always verify the included angle in SAS or the correct side in RHS.