Question

In the given figure, Δ ABC and Δ ABD are such that

AD = BC, ∠1 = ∠2 and ∠3 = ∠4. Prove that BD = AC.
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Answer 1

Answer:

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)