ABCD is a trapezium in which AB || CD and AD = BC. Show that : $\left(i\right)\angle A=\angle B\ \left(ii\right)\ \angle C\ =\angle D\ \left(iii\right)\ \Delta ABC\ \cong\Delta BAD$ (iv) diagonal AC = diagonal BD.

A triangle ABC is right angled at A. L is a point on BC such that AL ⊥ BC. Prove that ∠BAL=∠ACB

In fig M and N are two plane mirrors perpendicular to each other; prove that the incident ray CA is parallel to reflected ray BD.

If two parallel lines are intersected by a transversal, then prove that the bisectors of the interior angles form a rectangle.

In the given figure, if PQ ∥ PS, ∠SQR = 28° and ∠QRT = 65°,then find the values of x and y