Q:

Complete the proof.Given: AD || BC, AB ||CDProve: <B = <D​

Accepted Solution

A:
A B = C D ---------------- already given A D = B C ---------------- already given and  A C = A C ---------------- common Hence  Δ A B C ≡ Δ A C D ∴ ∠ D A C = ∠ B C A - both opposite equal sides  D C and  A B , and ∴ C D || A B - as alternate angles are equal ∴ ∠ D C A = ∠ C A B - both opposite equal sides  A D and  B C ∴ A D || B C - as alternate angles are equal As opposite sides of quadrilateral are parallel, A B C D is a parallelogram. Q . E . D .