AD and BC are equal and perpendiculars to a line segment AB. Show that CD bisects AB.

AD and BC are equal perpendiculars to a line segment AB (see the given figure) Show that CD bisects AB.

In the given figure, AB and DC are both perpendicular to line segment AD. BC intersects AD at P and P is the midpoint of AD. Prove that, ( 1 ) AB = CD ( 2 ) P is the midpoint of BC.

In triangle ABC , the bisector AD of angle A is perpendicular to side BC (see the given figure). Show that AB = AC and triangle ABC is isosceles.

OA and OB are two perpendicular straight lines. A straight line AB is drawn in such a manner that OA+OB=8 . Find the locus of the mid point of AB.

In triangle ABC, AD is the perpendicular bisector of BC (see the given figure). Show that triangle ABC is an isosceles triangle in which AB = AB .

AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is equidistant from A and B.

triangle ABC and triangle DBC are isosceles triangles on the same base BC. Prove that line AD bisects BC at right angles

In the figure, ΔABC and ΔABD are two triangles on the same base AB. If line segment CD is bisected by bar(AB) at O, show that ar (DeltaABC) = ar (DeltaABD).

In DeltaABC , the bisector AD of A is perpendicular to side BC Show that AB = AC and DeltaABC is isosceles.

AB is a line segment and line I is its perpendicular bisector. If a point P lies on I, show that P is equidistant from A and B.