Question

if ABCD is a quadrilateral in which AB//CD and AB=CD,then show that it is a parallelogram.

Answer 1

As you know angle sum of a quadrilateral = 360°
Hence, angles are: 36°, 60°, 108°, 156°


As all are right angles so the parallelogram is a rectangle

They want you to prove that AC = BD I suppose
AC = AB + BD + DC and therefore AC - BD = AB + DC = AB - CD = 0. done

Definition: A quadrilateral ABCD is a parallelogram if AB || CD and AD || BC. || means parallel.
That is the definiton. There is a proposition saying that if AB = CD and AD = BC, then we can prove that ABCD is a parallelogram. We just have to show that they are parallel.