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Course / Category - 6th Foundation NTSE

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6th Foundation NTSE

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Maths / Quadrilaterals / Properties of Square

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Properties of Square

Properties of Square:

A square is a rectangle with a pair of adjacent sides equal.

In other words, a parallelogram having all sides equal and each angle equal to a right angle is called a square.

Properties of a Square

All four interior angles are equal to 90°

All four sides of the square are congruent or equal to each other.

The opposite sides of the square are parallel to each other.

The diagonals of the square bisect each other at 90°

The two diagonals of the square are equal to each other.

Theorem: Each of the angle of a square is a right angle and all the four sides are equal.

Given: A square ABCD, such that AB = BC

To Prove: AB = BC = CD= DA and $angle$ A = $angle$ B= $angle$ C= $angle$ D= $90^0$

Proof: ABCD is a square. As every square is a parallelogram $Rightarrow$ ABCD is a ||gm.

$Rightarrow$ AB = CD and AD = BC [Opposite Parallelogram are equal]

But AB = BC [Given]

$Rightarrow$ AB = BC = CD= DA

Also ABCD is a square. As every square is a rectangle $Rightarrow$ ABCD is a rectangle.

$Rightarrow$ $angle$ A = $angle$ B= $angle$ C= $angle$ D= $90^0$ [ Each angle of rectangle is right angle]

Hence Proved

Illustration: PQRS is a square. Find the value of <SRP

Solution: Since PQRS is a square, PS = SR and $angle$ PSR = 90.

Now in $Delta PSR$ , we have PS = SR and $angle$ 1 = $angle$ 2 (Angles opposite to equal sides are equal)

But $angle$ 1 + $angle$ 2 + $angle$ PSR = 180 (Angle Sum Property)

2 $angle$ 1 + 90 = 180 [as $angle$ PSR = 90 Angle of a square is a right angle]

2 $angle$ 1 = 90

$angle$ 1 = 45

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Properties of Square

₹12300 ₹8000 +
Taxes