Question

Triangle ABC and triangle ABD are such that AD = BC. Angle 1 = Angle 2 and Angle 3= Angle 4. Prove that BD = AC

Answer 1

this is your answer

Answer 2

Answer with Step-by-step explanation:    

Given i) AD = BC

          ii) ∠1 = ∠2 and ∠3=∠4

Now ∠1+∠3 = ∠2+∠4 ⇒ ∠DAB= ∠CBA

Consider Δ ABC and Δ ABD

BC  = AD                            (Given)

∠CBA =∠DAB                    (Proved above)

AB= AB                              (Common)

∴ Δ ABC ≅ Δ BAD           (Side- Angle- Side)

⇒  AC = BD                       (C.P.C.T)