AD and BC are equal perpendiculars to a line segment AB (see Fig. 7.18). Show that CD bisects AB.

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

AD and BC are equal perpendicular to line segment AB. If DeltaBOC ~= DeltaAOD what is the relation between OC and OD ?

In Delta ABC , the bisector AD of angle A is perpendicular to side BC (see Fig. 7.27). Show that AB = AC and Delta ABC is isosceles.

In DeltaABC , AD is the perpendicular bisector of BC (See Fig. ). Show that DeltaABC is an isosceles triangle in which AB = AC.

In DeltaABC , AD is the perpendicular bisector of BC (See Fig. ). Show that DeltaABC is an isosceles triangle in which AB = AC.

Line-segment AB is parallel to another line-segment CD. O is the mid-point of AD (see Fig. 7.15). Show that (i) Delta AOB cong Delta DOC (ii) O is also the mid-point of BC.

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see Fig. 7.29). Show that AD = AE.

AB is a line-segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (see Fig. 7.37). Show that the line PQ is the perpendicular bisector of AB.

In quadrilateral ACBD, AC = AD and AB bisects angle A (see Fig. 7.16). Show that triangle ABC cong triangle ABD . What can you say about BC and BD?

If AB is a line segment AX and BY are two equal and line segments drawn on opposite sides of the line AB such that AX||BY. If the AB and XY intersect and each other at O, prove that AB and XY bisect each other.