Question

Q.1: 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:

Solution

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In △ABD and △BAC,

AD=BC (Given)

∠DAB=∠CBA (Given)

AB=BA (Common)

∴△ABD≅△BAC (By SAS congruence rule)

∴BD=AC (By CPCT)

And, ∠ABD=∠BAC (By CPCT)

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Solution To Question ID 463824

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Answer 2

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In △ABD and △BAC,

AD=BC (Given)

∠DAB=∠CBA (Given)

AB=BA (Common)

∴△ABD≅△BAC (By SAS congruence rule)

∴BD=AC (By CPCT)

And, ∠ABD=∠BAC (By CPCT)