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

In △ABC in given figure, the sides AB and AC of △ABC are produced to points E and D respectively. If bisectors BO and CO of ∠CBE and ∠BCD respectively meet at point O, then prove that ∠BOC = 90°   $-\frac{1}{2}$   ∠ A . 

If two lines intersect, prove that the vertically opposite angles are equal

In the given figure, ∠Q>∠R, PA is the bisector of ∠QPR and PM⊥QR. Prove that ∠APM =  $\frac{1}{2}$    (∠Q−∠R)

In given figure, DE || QR and AP and BP are bisectors of ∠EAB and ∠RBA respectively. Find ∠APB.

In fig the side AB and AC of △ ABC are produced to point E And D respectively. If bisector BO and CO of ∠CBE And ∠BCD respectively meet at point O, then prove that ∠ BOC =  $90^0-\frac{1}{2}$ ∠BAC