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

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 the given figure). Show that the line PQ is the perpendicular bisector of AB.

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.

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.

If P(x, y) is a point equidistant from the points A(6, -1) and B(2, 3), show that x-y = 3.

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

AB is a line segment and P is its midpoint. D and E are points on the same side of AB such that angle BAD = angle ABE and angle EPA = angle DPB (see the given figure). Show that:

If C is the middle point of AB and P is any point outside AB, then

Let P and Q be the points on the line joining A(-2, 5) and B(3, 1) such that AP = PQ=QB . Then, the mid-point of PQ is

Show that of all line segments drawn from a given point not on a given line, the perpendicular line segment is the shortest.

D is a point on side BC ΔABC such that AD = AC (see figure). Show that AB > AD.