Question

ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Fig. 7.17). Prove that: ∠ABD=∠BAC.

Answer 1

In Triangle ABD & BAC
AD=BC (Given)
Angle DAB = Angle CBA (Given)
AB=BA (Common In Both Triangles)
So , Triangle ABD Is Congruent To Triangle BAC (By SAS Criteria).
Hence , Angle ABD = Angle BAC (By C.P.C.T).

Answer 2

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Answer

Given,

AD = BC and ∠DAB = ∠CBA

(i) In ΔABD and ΔBAC,

AB = BA (Common)

∠DAB = ∠CBA (Given)

AD = BC (Given)

Therefore, ΔABD ≅ ΔBAC by SAS congruence condition.

(ii) Since, ΔABD ≅ ΔBAC

Therefore BD = AC by CPCT

(iii) Since, ΔABD ≅ ΔBAC

Therefore ∠ABD = ∠BAC by CPCT

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