Question

In the figure attached
AB is parallel to DC
Angle C = Angle D

Prove that
(i) AD = BC
(ii) AC = BD (means its diagonals)

Answer 1

in the fig, AB is parallel to DC and BC is the transversal
therefore angle B + angle D=180 (Interior pair of angles) ...(i)
similarly AB is parallel to DC and AD is the transversal
therefore angle A + angle D=180 (Interior pair of angles) ...(ii)
therefore from (i) and (ii) B+C=A+D but D=C therfore
B+D=A+D
B=A  that means A=B=C=D
therfore it is a rectangle therefore by property of rectangle
1. AD=BC (opposite side of a rectangle)and
2. AC=BD (diagonals of a rectangle are congruent)