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9th Foundation NTSE

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Maths / Quadrilaterals / Properties of Rectangle

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Properties of Rectangle

PROPERTIES OF RECTANGLE:

A parallelogram whose each angle is a right angle, is called a rectangle.

Theorem 1: Each of the four angles of a rectangle is a right angle.

Given: A rectangle ABCD in which $angle P = 90 ^0$

To Prove: $angle P = angle Q=angle R=angle S=90 ^0$

Proof: As each rectangle is a parallelogram and PQRS is a rectangle

Therefore PQRS is a parallelogram

$Rightarrow$ PQ || RS and PS is the transversal

$Rightarrow angle P +angle S = 180 ^0$ [Co-interior angles supplementary]

$Rightarrow 90^0 +angle S = 180 ^0Rightarrow angle S= 90^0$

Similarly we can prove that $angle R = 90 ^0; and; angle Q= 90^0$

Hence $angle P = angle Q=angle R=angle S=90 ^0$

Illustration: PQRS is a rectangle PQRS with $angle SRP= 27^0;find ;angle PRQ.$

Solution: PQRS is a rectangle and each angle on a rectangle is $90^0$

Therefore $angle R=90^0$

$angle SRP + angle PRQ=90^0$

Now $angle SRP=27^0$ [Given]

$27^0 + angle PRQ = 90^0$

$Rightarrow angle PRQ = 90-27 = 63^0$

Rectangle Properties

The fundamental properties of rectangles are:

A rectangle is a quadrilateral

The opposite sides are parallel and equal to each other

Each interior angle is equal to 90 degrees

The sum of all the interior angles is equal to 360 degrees

The diagonals bisect each other

Both the diagonals have the same length

A rectangle with side lengths a and b has the perimeter as 2a+2b units

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