class 8 Mathematics, chapter quadrilaterals

Chapter: Quadrilaterals – Class 8 Maths Notes

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🔷 What is a Quadrilateral?

A quadrilateral is a polygon with 4 sides, 4 angles, and 4 vertices.

The sum of the interior angles of any quadrilateral is always 360°.

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✏️ Parts of a Quadrilateral

Sides: The four line segments (e.g., AB, BC, CD, DA)

Vertices: The four corner points (A, B, C, D)

Diagonals: Line segments joining opposite corners (e.g., AC and BD)

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📐 Types of Quadrilaterals

Type of Quadrilateral Properties

Parallelogram - Opposite sides are equal and parallel<br>- Opposite angles are equal<br>- Diagonals bisect each other

Rectangle - All angles are 90°<br>- Opposite sides are equal and parallel<br>- Diagonals are equal and bisect each other

Square - All sides are equal<br>- All angles are 90°<br>- Diagonals are equal and bisect each other at 90°

Rhombus - All sides are equal<br>- Opposite angles are equal<br>- Diagonals bisect each other at 90°, but are not equal

Trapezium (Trapezoid) - Only one pair of opposite sides is parallel

Kite - Two pairs of adjacent sides are equal<br>- One pair of opposite angles is equal<br>- One diagonal bisects the other at 90°

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🧠 Important Angle Properties

Sum of the 4 interior angles of any quadrilateral = 360°

In a parallelogram:

Opposite angles are equal

Adjacent angles are supplementary (add up to 180°)

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🧮 Diagonals – Quick Reference

Quadrilateral Diagonals Are...

Rectangle Equal, bisect each other

Square Equal, bisect at 90°

Rhombus Bisect at 90°, not equal

Parallelogram Bisect each other

Kite One diagonal bisects the other at 90°

Trapezium No special property (except in isosceles trapezium – diagonals are equal)

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✨ Special Quadrilaterals Are Always...

Square is a rectangle, a rhombus, and a parallelogram.

Rectangle and Rhombus are types of parallelograms.