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ABCD is a quadrilateral in which AD = BC and ?DAB = ?CBA. Prove that ?ABD ? ?BAC.

Maths Science Expert

Dear Sarath, let me correct your question, you put ? instead of So correct question should be: ABCD is a quadrilateral in which AD = BC and DAB = CBA. Prove that ABD = BAC. Solution: In ABD & BAC, Given: AD=BC DAB= CBA To Prove That: ABD = BAC Proof: AB = BA (Common) DAB... read more
Dear Sarath, let me correct your question, you put ? instead of ∠ So correct question should be: ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that ∠ABD = ∠BAC. Solution: In ΔABD & ΔBAC, Given: AD=BC ∠DAB=∠CBA To Prove That: ∠ABD = ∠BAC Proof: AB = BA (Common) ∠DAB = ∠CBA (Given) AD = BC (Given) Hence, ΔABD ≅ ΔBAC. ( by SAS congruence rule). So, ∠ABD = ∠BAC (by CPCT) [Hence Proved] read less

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From side angle sode (SAS) congruency criteria you can prove DAB & CBA are congruent (as AD=BC, ?DAB=?CBA & AB is the common side. ) As a result, we can say that ?ABD=?BAC

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