Question

In quadrilateral ABCD, AD = BC and angle DAB = angle CBA. If triangle ABD congruent to triangle BAC. The relation between angle ABD and angle BAC is : (a) angle ABD > angle BAC (b) angle ABD < angle BAC. (c) angle ABD = angle BAC. (d) angle ABD = (1/2) angle BAC

Answer 1

Given:

In quadrilateral ABCD,

AD = BC &

∠DAB = ∠CBA

 

To Prove:

(i)              ΔABD ≅ ΔBAC

(ii)            BD=AC

(iii)           ∠ABD = ∠BAC

 

Proof:

i)

In ΔABD & ΔBAC,

AB = BA    (Common)

∠DAB = ∠CBA  (Given)

AD = BC (Given)

Hence, ΔABD ≅ ΔBAC.        

( by SAS congruence rule).

(ii) Since, ΔABD ≅ ΔBAC

Then, BD = AC                                       ( by CPCT)

(iv)   Since, ΔABD ≅ ΔBAC

Then , ∠ABD = ∠BAC                         (by CPCT)

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Hope this will help you.....

Answer 2

Answer:

Option C Angle ABD = Angle BAC

Step-by-step explanation:

A = B

D = C

angle ABD = angle BAC

Because

AB = BA

BD = AC

Hence All The Sides Are Equal

So, angle ABD = angle BAC