Question

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

Answer 1

Answer:

Explanation:

Ans. (i) In quadrilateral ABCD, we have

AD = BC and              

∠DAB = ∠CBA.                

In ΔABD and ΔBAC,                

AD = BC[Given]                

AB = BA[Common]              

∠DAB = ∠CBA[Given]                

∴ Using SAS criteria, we have ΔABD ≌ ΔBAC        

(ii) ∵ ΔABD ≌ ΔBAC              

∴ Their corresponding parts are equal.              

 ⇒ BD = AC        

 (iii) Since ΔABD ≌ ΔBAC                ∴ Their corresponding parts are equal.                ⇒ ∠ABD = ∠BAC.