In the given figure, ΔABC and ΔABD are such that AD = BC, ∠1 = ∠2 and ∠3 = ∠4. Prove that BD = AC.

Question

In the given figure, ΔABC and ΔABD are such that AD = BC, ∠ 1 = ∠ 2 and ∠ 3 = ∠ 4. Prove that BD = AC.

Philoid · Accepted Answer

Taking ΔABC and ΔABD in consideration-

AD = BC

Since, it is given that

∠1 = ∠2 and ∠3 = ∠4

Adding them –

∠1 + ∠3 = ∠2 + ∠4.

= ∠DAB = ∠ABC

And AB is the common side on both triangle.

So, by side angle side(SAS) criteria-

Triangle ΔABC and ΔABD are congruent.

So, BD = AC (by congruency criteria).