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.

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.

P is a point equidistant from two lines l and m intersecting at point A (see Fig. 7.38). Show that the line AP bisects the angle between them.

P is a point equidistant from two lines l and m intersecting at point A (see Fig. ). Show that the line AP bisects angleBAC .

P is a point equidistant from two lines l and m intersecting at point A (see Fig. ). Show that the line AP bisects angleBAC .

AB is a line segment and P is its midpoint. D and E are points on the same side of AB such that angleBAD = angleABE and angleEPA = angleDPB . Show that AD=BE.

Show that the line segments joining the mid-points of opposite sides of a quadrilateral bisect each other.

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.

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 triangleAOXequivtriangleBOY .

Line segment joining the mid-points of the opposite sides of a quadrilateral ............. each other.