Question

ABCD is a quadrilateral in which AB||DC and AD=BC. Prove that angle A = angle B and angle C=angle D

Answer 1

for angle C =angle D

angle A + angle D = 180 .....3
angle ABC + angle BCD = 180 .......4
equating 3 and 4

A + D = B + C
A + C = A + D ( because Angle A = angle B)
hence angle C = D