CBSE 8 Maths Chapter 4 CBSE Class 8 Maths Notes Chapter 4 Quadrilaterals Notes 2025-26

Quadrilaterals are shapes with four sides and four angles. The word 'quadrilateral' itself comes from Latin, with 'quadri' meaning four and 'latus' meaning sides. In this chapter, you'll learn about different types of quadrilaterals, their properties, and how to identify or construct them, all of which are essential in geometry for Class 8 Maths.

Definition and Classification of Quadrilaterals Every shape with four straight sides and four angles is called a quadrilateral. These sides usually meet at their endpoints to form closed figures. Rectangles, squares, parallelograms, rhombuses, kites, and trapeziums all fall under this category. Each type has features that make it unique, such as side lengths, angles, and how their opposite sides or angles relate to each other.

Rectangles A rectangle is a quadrilateral where all four angles are right angles (90°), and the opposite sides are equal in length. Another way to define a rectangle is by its diagonals: a quadrilateral in which both diagonals are equal and bisect each other is also a rectangle. Key properties of a rectangle include:

• All angles are 90°.
• Opposite sides are equal and parallel.
• Diagonals are equal in length and bisect each other.

Squares A square is a special type of rectangle where all four sides are equal in length, and every angle is 90°. This means every square is a rectangle, but not all rectangles are squares. For a square:

• All sides are equal.
• All angles are 90°.
• Diagonals are equal, bisect each other at 90°, and also bisect the angles of the square.
• Opposite sides are parallel.

If you know the length of a square's diagonal, you can construct it by ensuring the diagonals are equal, cross at 90°, and meet in the center.

Sum of Angles in a Quadrilateral No matter what type of quadrilateral you have, the sum of its four angles is always 360°. This important property results from dividing any quadrilateral into two triangles; since each triangle has angle sum 180°, together it's 360°.

Parallelogram A parallelogram is a quadrilateral where both pairs of opposite sides are parallel. Parallelograms might look slanted compared to rectangles and squares, but they follow some predictable rules:

• Opposite sides are equal and parallel.
• Opposite angles are equal. Adjacent angles add up to 180°.
• Diagonals bisect each other but are not always equal in length.

Rectangles, squares, and rhombuses are all specific types of parallelograms, each with extra requirements.

Rhombus A rhombus is another variety of parallelogram in which all the sides are equal in length. However, unlike a square, the angles do not have to be 90°. The main features include:

• All four sides are equal and opposite sides are parallel.
• Diagonals intersect at 90°, bisect each other, and also bisect the angles of the rhombus.
• Opposite angles are equal; adjacent angles add up to 180°.

Kite and Trapezium A kite is a quadrilateral where two pairs of adjacent sides are equal. A unique feature is that one of the diagonals (the longer one) bisects the other diagonal at 90° and also splits the angles at its ends into two equal parts.

A trapezium is a quadrilateral having only one pair of parallel sides. If the non-parallel sides are equal, it's known as an isosceles trapezium and has a special property where the base angles (angles next to each parallel side) are also equal.

• In kites: two distinct pairs of equal adjacent sides; longer diagonal is perpendicular and bisects the shorter diagonal.
• In trapeziums: exactly one pair of sides is parallel; isosceles type has equal non-parallel sides and equal base angles.

Quick Comparison Table

• If a quadrilateral has three right angles, the fourth angle must also be 90°, so it's a rectangle.
• The diagonals of parallelograms always bisect each other, but are only equal in rectangles or squares.
• All squares are rectangles, parallelograms, and rhombuses at the same time.
• Every quadrilateral, no matter how "tilted," adds up to 360° in angles—even if some angles are greater than 180° (reflex angles).

Activities & Practice Examples

• Construct quadrilaterals using threads, sticks, or drawing tools based on properties like side lengths or diagonals and their intersections.
• Try joining two triangles with equal or different sides to create different quadrilaterals and identify their properties in your drawing.
• Check and prove whether statements about quadrilaterals (like "All kites are rhombuses") are true or false using figures or property checks.
• Fold paper into different shapes and study the patterns and creases to see new quadrilaterals forming.

Summary

• Quadrilaterals include squares, rectangles, parallelograms, rhombuses, kites, and trapeziums, each with distinct angle and side properties.
• The sum of the angles in any quadrilateral is 360°.
• Understanding the properties of each quadrilateral helps you identify them easily and solve geometry problems effectively.

CBSE Class 8 Maths Notes Chapter 4 Quadrilaterals Notes – Important Revision Concepts

These concise Class 8 Maths Chapter 4 Quadrilaterals revision notes cover all major types of quadrilaterals—rectangles, squares, parallelograms, rhombuses, kites, and trapeziums. With clear definitions and key properties, students can easily review and strengthen their understanding of this important geometry topic.

Use these notes for last-minute revision to quickly recall properties of quadrilaterals, facts about diagonals, and angle sums in quadrilaterals. The simple format and well-organized points make these notes handy for quick reference and efficient exam preparation.