0Class 8 Mathematics – Quadrilaterals
1. Introduction
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A quadrilateral is a polygon with four sides and four angles.
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The sum of all interior angles of a quadrilateral is always 360°.
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Quadrilaterals are widely used in geometry, construction, and design.
Key Concept:
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Four sides → four vertices → four interior angles.
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Shape depends on lengths of sides and size of angles.
2. Types of Quadrilaterals and Their Properties
| Type | Description & Properties | Special Features |
|---|---|---|
| Square | All sides equal; all angles 90°; diagonals equal and bisect each other at right angles | Regular quadrilateral |
| Rectangle | Opposite sides equal; all angles 90°; diagonals equal and bisect each other | Parallelogram with right angles |
| Rhombus | All sides equal; opposite angles equal; diagonals bisect at right angles | Parallelogram with equal sides |
| Parallelogram | Opposite sides equal and parallel; opposite angles equal; diagonals bisect each other | Tilted rectangle/rhombus |
| Trapezium | Only one pair of opposite sides parallel; angles adjacent to parallel sides are supplementary | Can be isosceles (non-parallel sides equal) |
| Kite | Two pairs of adjacent sides equal; one pair of opposite angles equal; diagonals intersect at right angles | Symmetrical along one diagonal |
3. Angles in Quadrilaterals
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Sum of interior angles: 360°
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Sum of exterior angles: 360°
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In special quadrilaterals:
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Square/Rectangle: All angles are 90°
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Rhombus/Parallelogram: Opposite angles are equal
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Kite: One pair of opposite angles equal
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Angles are useful in geometry proofs and construction.
4. Key Points to Remember
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Quadrilateral = 4 sides + 4 angles
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Sum of interior angles = 360°
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Types based on sides and angles: Square, Rectangle, Rhombus, Parallelogram, Trapezium, Kite
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Diagonals and symmetry help in identifying the type.
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Understanding properties is essential for geometry problems and constructions.
