Question

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

Answer 1

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Given,

AD = BC - - - - - - - - - - - 1 (given)

∠DAB = ∠CBA - - - - - - - - - - 2 (given)

AB = AB - - - - - - - - - - - - - - - 3 (common)

1)) ΔABD ≅ ΔBAC

By C.P.C.T we can say that all angles and sides of a triangle will also be equal

2))BD = AC

By C.P.C.T, we can say that BD = AC

3))∠ABD = ∠BAC

By C.P.C.T, we can say that ∠ABD = ∠BAC

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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