Question

If ABC is a quadrilateral in which AB ||CD and AD =BC, prove that <A=<B. ​

Answer 1

see the attached figure ,

given , 

AB = CD 

AD = BC

to prove that : ABCD is a IIgram

proof :- AB = CD (from the given )

             BC = AD (from the given )

             BD = BD (common side )

∴ Δ ADB ≡ Δ DBC by SSS congruence rule . 

therefore from CPCT we can write that ∠ADB = ∠ DBC (alternate interior angle )

since the alternate interior angles and opposite sides are equal in a quadrilateral therefore it is a IIgram . 

 i hope it helps ...........................^_^

Answer 2

hey mate, I am parth dhami