Question

In quadrilateral ABCD, AD = BC and BD = CA.
Prove that:
(i) ∠ADB = ∠BCA
(ii) ∠DAB = ∠CBA

Answer 1

Given: In quadrilateral ABCD, AD = BC and BD = AC.

To Prove:

(i) ∠ADB = ∠BCA
(ii) ∠DAB = ∠CBA

Proof:

In ΔABD and ΔBAC,
AD = BC           ....(given)
BD = CA           ....(given)
AB = AB           ....(common)

∴ ΔABD ≅ ΔBAC ....(by SSS congruence criterion)

`{:(∠"ADB" = ∠"BCA"), (∠"DAB" = ∠"CBA"):}} ...("c.p.c.t.")`