NCERT Class 8 Maths Chapter 4
Quadrilaterals
NCERT Class 8 Maths Chapter 4 (Ganita Prakash) explores quadrilaterals — four-sided polygons — their properties, classification, and special types. This CBSE chapter covers parallelograms, rectangles, rhombuses, squares, trapeziums, and kites, explaining the unique properties of each. Students learn to prove properties using angle-sum relationships and use these in solving geometric problems.
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Key Terms
- Quadrilateral
- A polygon with four sides, four angles, and four vertices; the sum of interior angles of any quadrilateral is 360°.
- Parallelogram
- A quadrilateral where opposite sides are parallel and equal, and opposite angles are equal; diagonals bisect each other.
- Rectangle
- A parallelogram where all angles are 90°; diagonals are equal in length and bisect each other.
- Rhombus
- A parallelogram where all four sides are equal; diagonals bisect each other at right angles.
- Square
- A quadrilateral that is both a rectangle and a rhombus — all sides equal and all angles 90°; diagonals are equal and bisect each other at right angles.
- Trapezium
- A quadrilateral with exactly one pair of parallel sides (called bases); the parallel sides may be of different lengths.
- Kite
- A quadrilateral with two pairs of adjacent (not opposite) equal sides; diagonals are perpendicular to each other.
Frequently Asked Questions
What is the angle sum property of a quadrilateral Class 8?▾
The sum of all interior angles of any quadrilateral is 360°. This can be proved by drawing a diagonal to divide the quadrilateral into two triangles, each having an angle sum of 180°. So total = 180° + 180° = 360°. This property is used extensively in NCERT Class 8 Maths Chapter 4 to find missing angles.
What are the properties of a parallelogram Class 8 Maths?▾
Properties of a parallelogram: (1) Opposite sides are equal and parallel, (2) Opposite angles are equal, (3) Consecutive angles are supplementary (add up to 180°), (4) Diagonals bisect each other (cut each other into two equal halves), (5) Each diagonal divides the parallelogram into two congruent triangles.
What is the difference between a rhombus and a square Class 8?▾
Both a rhombus and a square have all four sides equal, and both have diagonals that bisect each other at right angles. The key difference: a square has all angles equal to 90° (it is also a rectangle), while a rhombus has opposite angles equal but not necessarily 90°. A square is a special rhombus.
What is the difference between a rectangle and a parallelogram Class 8 NCERT?▾
All rectangles are parallelograms, but not all parallelograms are rectangles. A parallelogram has opposite sides equal and parallel with opposite angles equal. A rectangle is a parallelogram where all four angles are 90°. Additionally, in a rectangle the diagonals are equal in length (unlike a general parallelogram where they are not equal).
What are the properties of a trapezium Class 8?▾
A trapezium has exactly one pair of parallel sides (called bases). The non-parallel sides are called legs. In an isosceles trapezium, the legs are equal, base angles are equal, and diagonals are equal. The area of a trapezium = ½ × (sum of parallel sides) × height.
How are quadrilaterals classified Class 8 Science?▾
Quadrilaterals are classified based on their properties: (1) Trapezium — one pair of parallel sides, (2) Parallelogram — two pairs of parallel sides, (3) Rectangle — parallelogram with all right angles, (4) Rhombus — parallelogram with all equal sides, (5) Square — both rectangle and rhombus, (6) Kite — two pairs of adjacent equal sides. Every square is a rectangle, rhombus, and parallelogram.
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