l is the perpendicular bisector of the line segment PQ and R is a point on the some side of l as P. The line segment QR intersects l at X. Prove that `PX + XR = QR`.

Find the equation of the perpendicular bisector of the line segment joining the points (7, 4) and (-1, -2).

Prove that the line segment joining the middle point of two sides of a triangle is parallel to the third side.

ABCD is a parallelogram. E is any point on the side BC, line segment drawn through D and E cards the extended AB at T Prove that DE * EB = CE * TE .

M is the mid point of the side CD of the parallelogram ABCD. The line BM is drawn intersecting AC in L and AD produced Prove that (i) ALxxLM=CLxxBL

M is the mid point of the side CD of the parallelogram ABCD. The line BM is drawn intersecting AC in L and AD produced at E.Prove that(ii) EL = 2BL

Find the ratio in which the line segment joining the points (2,-3) and (4,6) is divided by the x-axis.

Prove that line segment joining the middle points of two non-parallel sides of a trapezium is parallel to the parallel sides.

Find the ratio in which the point of intersection of the x-axis and the line segment which joins the points (3,5) and (2,-7) internaly divides the line segment.Also find the coordinates of the point.

prove by using the principle of similar triangles that: the line segment drawn parallel to the side of a triangle divides the other sides proportionally.

if(2, P) is the mid-point of the line segment joining to the point A(6,-5) and B(-2,11), find the value of P.