Question

ΔABC and ΔDEF are two triangles in which AB = DF, ∠ACB = 70°, ∠ABC = 60°, ∠DEF = 70° and ∠EDF = 60°. Prove that the triangles are congruent

Answer 1

In ΔABC ∠B = 60° and ∠C = 70°

∴ ∠A = 180° – (60° + 70°)

= 180° – 130°

= 50°

In ΔDEF ∠E = 70° and ∠D = 60°

∠F = 180° – (70° + 60°)

= 180° – 130°

= 50°

∠A = ∠F = 50°

∠B = ∠D = 60°

∠C = ∠E = 70°

By AAA congruency

ΔABC ≅ ΔFDE

or

∠B = ∠D = 60°

∠C = ∠E = 70°

AB = FE

By ASA congruency

ΔABC ≅ ΔFDE