Question

ABCD is a quadrilateral in which AD=BC and DAB=CBA

Answer 1

Correct Question :-

ABCD is a quadrilateral in which AD=BC and ∠DAB = ∠CBA. Prove that

(i)△ABD ≅ △BAC

(ii) BD = AC

(iii) ∠ABD = ∠BAC

Solution :-

(i) In△ABD and △BAC

AD = BC (Given)

∠DAB = ∠BAC (Given)

AB = AB (Common)

∴ △ABD ≅ △BAC (SAS Criteria)

(ii) BD = AC

∵ △ABD ≅ △BAC

∴ BD = AC (CPCT)

(iii) ∠ABD = ∠BAC

∵ △ABD ≅ △BAC

∴ ∠ABD = ∠BAC (CPCT)

Answer 2

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ABCD is a quadrilateral in which AD=BC and ∠DAB = ∠CBA. Prove that

(i)△ABD ≅ △BAC

(ii) BD = AC

(iii) ∠ABD = ∠BAC

$\huge \pink \star{ \green{ \boxed{ \boxed{ \boxed{ \purple{ \mathfrak{Solution :-}}}}}}} \pink\star$

(i)△ABD ≅ △BAC

In△ABD and △BAC

AD = BC (Given)

∠DAB = ∠BAC (Given)

AB = AB (Common)

∴ △ABD ≅ △BAC (SAS Criteria)

(ii)BD = AC

as,△ABD ≅ △BAC

∴ BD = AC (CPCT)

(iii) ∠ABD = ∠BAC

as, △ABD ≅ △BAC

∴ ∠ABD = ∠BAC (CPCT)

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