Triangles — Important Questions

SSS, SAS, ASA, RHS

Valid congruence criteria are: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and RHS (Right angle-Hypotenuse-Side). AAA only ensures similarity, not congruence. SSA is not a valid criterion as it can lead to ambiguous cases.

70°

By the exterior angle theorem, an exterior angle equals the sum of the two non-adjacent interior angles. So: Exterior angle = Sum of two opposite interior angles. 120° = 50° + other angle. Therefore, other angle = 120° - 50° = 70°.

PQ = 5 cm, QR = 7 cm, ∠A = ∠P, Area of ABC = Area of PQR

When triangles are congruent (ABC ≅ PQR), corresponding parts are equal: AB = PQ = 5 cm, BC = QR = 7 cm, ∠A = ∠P, ∠B = ∠Q (not ∠R), ∠C = ∠R. Congruent triangles have equal areas.

1

A triangle can have at most one obtuse angle. If a triangle had two obtuse angles, their sum would exceed 180° (since each obtuse angle > 90°), but the sum of all three angles in a triangle must be exactly 180°. Therefore, maximum one obtuse angle is possible.