Mathematics
ABCD is a parallelogram. What kind of quadrilateral is it if :
(i) AC = BD and AC is perpendicular to BD ?
(ii) AC is perpendicular to BD but is not equal to it ?
(iii) AC = BD but AC is not perpendicular to BD?
Answer
(i) It is given that AC = BD and AC is perpendicular to BD.
That is, the diagonals of the parallelogram are equal and perpendicular to each other.
Hence, the parallelogram is a square.
(ii) It is given that AC is perpendicular to BD but is not equal to it.
That is, the diagonals of the parallelogram are perpendicular to each other but not equal to each other.
Hence, the parallelogram is a rhombus.
(iii) It is given that AC = BD but AC is not perpendicular to BD.
That is, the diagonals of the parallelogram are equal but not perpendicular.
Hence, the parallelogram is a rectangle.
Related Questions
Given : Parallelogram ABCD in which diagonals AC and BD intersect at M.
Prove : M is the mid-point of LN.
In an isosceles-trapezium, show that the opposite angles are supplementary.
Prove that the diagonals of a parallelogram bisect each other.
If the diagonals of a parallelogram are of equal lengths, the parallelogram is a rectangle. Prove it.