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.

In Fig. AC = AE, AB = AD and angleBAD = angleEAC . Show that BC = DE.

In Fig. AC = AE, AB = AD and angleBAD = angleEAC . Show that BC = DE.

In fig. D and E are points on side BC of triangleABC such that BD=CE and AD=AE. Show that triangleABDequivtriangleACE

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.

D and E are points on sides AB and AC respectively of a DeltaABC such that ar (DeltaBCE) = ar (DeltaBCD) . Show that DE || BC .

D and E are points on sides AB and AC respectively of DeltaABC such that ar (DBC) = ar (EBC). Prove that DE II BC .

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 .

ABC is an isosceles triangle with AB=AC and D is a point on an BC such that ADbotBC to prove that angleBAD=angleCAD ,