Prove that diagonals of trapezium cut each other proportionally.

Show that the diagonals of a quadrilateral bịsect each other if and only if it is a parallelogram.

The points 'A(6,1), B(8,2), C(9,4)', D '(p, 3)' are the vertices of a parallelogram. Find the value of p using the concept that the diagonals of a parallelogram bisect each other

The length of a diagonal of square is 4 cm . a) What is its area? b) The length of a diagonal of a square is d units and its area is A sq.units. Write the relation between them? c) Which is the proportionality constant?

In the picture below, the diagonals of the trapezium ABCD intersect at P. Prove that PAtimesPD=PBtimesPC . .

Prove that any non-isosceles trapezium is not cyclic.

Given statement in (a) and (b). Identify the statements given below as contrapositive or converse of each other . If the quadrilateral is a parallelogram then its diagonals bisect each other 1 )If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram 2) if the diagonals of a quadrilateral bisect eachother , then it is a parallogram

Prove that for any quadrilateral with diagonals perpendicular, the area.ls half the product of the diagonals:

Prove that in any parallelogram, the 'sum of the squares of all sides is equal to the sum of the squares of the diagonals'.

The perpendicular from the square corners of a right angle triangle cuts the opposite side into two parts of 2 and 3 cm length.Prove that two small triangles cut by the perpendicular have the same angles.