Question

Question 12 (ii)
ABCD is a trapezium in which AB || CD and AD =BC (see the given figure). Show that $\angle C=\angle D$.

Answer 1

AB || CD.
$\angle A+\angle D={180}^{\circ }$ ( Angles on the same side of the transversal).
Also, $\angle C+\angle B={180}^{\circ }$ ( Angles on the same side of the transversal).
$\angle A+\angle D=\angle C+\angle B$.
However, $\angle A=\angle B$ [Using the result obtained in (i)].
$\therefore \angle C=\angle D$.