QUADRILATERAL
Quadrilateral
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A quadrilateral is a closed figure.
The most important property of quadrilateral is
The sum of the interior angles of a quadrilateral is 360⁰.
∠A + ∠B + ∠C + ∠D = 360⁰.
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Types of Quadrilateral
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Convex Quadrilateral
If each angle of quadrilateral is less than 180⁰, then it is called a convex quadrilateral
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Concave Quadrilateral
If at least one angle of quadrilateral is more than 180⁰, then it is called a concave quadrilateral
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Types of Quadrilateral
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Trapezium : A trapezium is a quadrilateral in which one pair of opposite sides are parallel whereas the other pair of opposite sides are non-parallel
· ∠A + ∠B + ∠C + ∠D = 360⁰.
· AB and DC are parallel
· AD and BC are not parallel
· ∠A and ∠D are co-interior angles.
· ∠B and ∠C are co-interior angles.
· ∠A + ∠D = 180⁰
· ∠B + ∠C = 180⁰
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Isosceles Trapezium: If the non parallel sides of trapezium are equal then it is called Isosceles Trapezium.
· ∠A = ∠B and ∠C =∠D
· ∠A + ∠D = 180⁰ and ∠B + ∠C = 180⁰
· ∠A + ∠C = 180⁰ and ∠B + ∠D = 180⁰
· Diagonal AC = diagonal BD
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Parallelogram: A parallelogram is a quadrilateral in which both the pairs of opposite sides are parallel.
· Opposite sides are equal. AB = DC and AD = BC
· Opposite angles are equal ∠A = ∠C and ∠B =∠D
· Adjacent angles are supplementary i.e.
o ∠A + ∠B = 180⁰
o ∠B + ∠C = 180⁰
o ∠C + ∠D = 180⁰
o ∠D + ∠A = 180⁰
· Diagonals bisect each other. If diagonals AC and BD intersect each other at point O then OA=OC = ½ (AC) and OB=OD = ½(BD)
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Rectangle: A rectangle is a quadrilateral in which every angle is 90⁰ ( a right-angle)
· ∠A = ∠B = ∠C = ∠D = 90⁰
· Opposite sides are equal. AB = DC and AD = BC
· Opposite sides are parallel
· AB || DC and AD ||BC
· Diagonals are equal, AC = BD
· Diagonals bisect each other. If diagonals AC and BD intersect each other at point O then OA=OC = ½ (AC) and OB=OD = ½(BD)
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Rhombus :
· A quadrilateral with all the sides equal is called a rhombus. AB=BC=CD=DA
· A quadrilateral is a rhombus, if its diagonals bisect each other at 90⁰
· A parallelogram with any pair of adjacent sides equal is a rhombus.
· In a rhombus, diagonals bisect the angles at vertex
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Square : A square is a quadrilateral in which
· All the sides are equal AB=BC=BC=DC
· Each angle is 90⁰ ∠A = ∠B = ∠C = ∠D = 90⁰
· Diagonals are equal and bisect each other at 90⁰
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