Question

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

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given :

AD = BC

∠DAB = ∠CBA

To Prove :

ΔABD ≅ ΔBAC

  BD = AC

∠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}Hence∗Proved