Question

ABCD is a quadrilateral in which AD=BC and angle DAB=angle CBA.Prove that BD=AC

Answer 1

Given: AD=BC, angle DAB= angle CBA

To Prove: Δ ABD ≅ Δ BAC, BD = AC, ∠ ABD = ∠ BAC

Proof: In triangle ABD and Triangle BAC,

AD = BC (given)

∠ DAB = ∠ CBA (given)

AB = BA (common)

therefore, Δ ABD ≅ Δ BAC (SAS rule)

BD = AC (CPCT)

∠ ABD = ∠ BAC (CPCT)

Hence Proved

Answer 2

see that picture and you will get the answer