Question

AD = BC and BD = AC , prove that ∠DAB = ∠CBA

Answer 1

In ∆ABC & ∆BAD
BC=AD. (GIVEN)
AC=BD. (GIVEN)
AB=AB. (Common)
By SSS congruency
∆ABC≈∆BAD
angle CBA=angle DAB
Here ≈=congruent

Answer 2

Answer:

To prove:

(i) ∠ADB=∠BCA

(ii) ∠DAB=∠CBA

Proof: in △ADB and △ACB

AB=AB (Common)

AD=BC (given)

DB=AC (given)

△ADB≅△ACD (SSS axiom)

∠ADB=∠BCA

∠DAB=∠CBA