Diagonals of a Rectangle Are of Equal Length
Diagonals of a Rectangle Are of Equal Length
Theorem 2: The diagonals of a rectangle are of equal length.
Given : PQRS is a rectangle. To Prove : PR = QS Proof:As each rectangle is a parallelogram and PQRS is a rectangle Therefore PQRS is a parallelogram PS = QR '................(1) [ Opposite sides of a parallelogram] As each angle of a rectangle is a right angle In PS = QR [ From Equation 1 ] RS = RS [ Common ]
Hence Proved |  |
Converse of Theorem 2: If the diagonals of a parallelogram are of equal length, it is a rectangle.
Given : PQRS is a parallelogram such that PR = QS. To Prove : PQRS is a rectangle Proof: In PR = QS [ Given ] PS = QR [ Opposite sides of parallelogram ] RS = RS [ Common ]
As PQRS is a parallelogram, PS || QR Now PS || QR and RS is the transversal
Now PQRS is a parallelogram in which one angle is a right angle. Therefore PQRS is a rectangle Hence Proved | |
Illustration: The diagonals of a rectangle PQRS intersect at O, If
Solution: PQRS is a rectangle and we know that diagonals of a rectangle are equal Each rectangle is aparallelogram and we know that diagonals of a parallelogram bisect each other Therefore OS = OR [ Because when diagonals are equal halves are equal ] In
Now
Now each angle of a rectangle is a right angle. |
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The diagonals of a rectangle PQRS intersect at O, If | |||
| Right Option : A | |||
| View Explanation | |||
The diagonals of a rectangle are ____________ . | |||
| Right Option : A | |||
| View Explanation | |||
ABCD is a rectangle with | |||
| Right Option : D | |||
| View Explanation | |||
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