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Diagonals of a Rectangle Bisect Each-Other and Are Equal

In which of t...

Question

In which of the following figures are the diagonals equal?

(a) Parallelogram

(b) Rhombus

(c) Trapezium

(d) Rectangle

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Solution

ANSWER:
(d) Rectangle.
The diagonals of a rectangle are equal.

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Q. The two diagonals are equal in a

(a) parallelogram

(b) rhombus

(c) rectangle

(d) trapezium

The two diagonals are not necessarily equal in a

(a) rectangle (b) square

(c) rhombus (d) isoceles trapezium

If the diagonals of a quadrilateral bisect each other at right angles then the figure is a

(a) trapezium

(b) parallelogram

(c) rectangle

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Q. Which of the quadrilaterals mentioned in brackets have the following properties?

(1) Diagonals are congruent. (square, rectangle, rhombus)
(2) The longer diagonal is the perpendicular bisector of the shorter and the shorter of the longer. (trapezium, kite, rhombus)
(3) All sides and angles are congruent. (rhombus, square, rectangle)
(4) Opposite angles are congruent. (kite, parallelogram, rectangle)
(5) Opposite sides are congruent. (trapezium, rectangle, parallelogram)
(6) Diagonals bisect each other at right angles. (square, rectangle, rhombus)
(7) Diagonals bisect each another. (rectangle, parallelogram, kite)
(8) One pair of opposite sides is parallel. (kite rhombus trapezium)

Q. Which of the following statements are true and which are false?
(i) The diagonals of a parallelogram are equal.
(ii) The diagonals of a rectangle are perpendicular to each other.
(iii) The diagonals of a rhombus are equal.
(iv) Every rhombus is a kite.
(v) Every rectangle is a square.
(vi) Every square is a a parallelogram.
(vii) Every square is a rhombus.
(viii) Every rectangle is a parallelogram.
(ix) Every parallelogram is a rectangle.
(x) Every rhombus is a parallelogram.

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Diagonals of a Rectangle Bisect Each-Other and Are Equal

Standard IX Mathematics

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