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?
Quadrilaterals
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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.
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