Question

In the given figure, ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that (i) ΔABD ≅ ΔBAC (ii) BD = AC (iii) ∠ABD = ∠BAC

Answer 1

Given :

• AD = BC
• ∠DAB = ∠CBA

To Prove :

1. ΔABD ≅ ΔBAC
2.   BD = AC
3. ∠ABD = ∠BAC

Proof :

→_→ In ΔABD and ΔBAC

⇒ AD = BC            [Given]

⇒ ∠DAB = ∠CBA   [Given]

⇒ AB = BA             [Common]

∴ ΔABD ≅ ΔBAC   [SAS CONGRUENCE]

∴ BD = AC              [CPCT]  

∴ ∠ABD = ∠BAC    [CPCT]

$\huge\boxed{Hence*Proved}$

Answer 2

Step-by-step explanation:

ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (See the given figure). Prove that (i) ΔABD ≅ ΔBAC (ii) BD = AC (iii) ∠ABD = ∠BAC.

Class 9 - Math - Triangles Page 119"