Revision Notes: Class 8 Maths Chapter 4 Quadrilaterals

Class 8 Maths Chapter 4: Quadrilaterals — Quick Revision Notes

• Angle Sum Property: the four interior angles of any simple quadrilateral always sum to 360° — proved by splitting it into two triangles with a diagonal.
• Rectangle: all angles 90°, opposite sides equal; diagonals are equal and bisect each other (not necessarily perpendicular).
• Square: a rectangle with all sides equal; diagonals are equal, bisect each other, are perpendicular, and bisect the vertex angles (each 90° corner splits into two 45° angles).
• Parallelogram: both pairs of opposite sides parallel; any ONE of these is sufficient to prove it: opposite sides equal, opposite angles equal, or diagonals bisect each other.
• Rhombus: a parallelogram with all four sides equal; diagonals are perpendicular bisectors of each other and bisect the vertex angles, but aren’t necessarily equal.
• Kite: two distinct pairs of adjacent equal sides; one diagonal is the perpendicular bisector of the other, but diagonals are unequal and it’s generally not a parallelogram.
• Trapezium: exactly one pair of parallel sides; co-interior angles on the parallel sides sum to 180°. An isosceles trapezium has equal legs and equal base angles but is NOT a parallelogram.
• Family hierarchy: square ⊂ rectangle ⊂ parallelogram; square ⊂ rhombus ⊂ kite; parallelogram ∩ kite = rhombus; rectangle and kite never overlap (except the trivial square case).
• Proof method: most properties are proved using triangle congruence (SSS, SAS, ASA) after drawing a diagonal — measurement alone only suggests a conjecture, not a proof.
• Common traps: perpendicular diagonals alone do NOT guarantee a rhombus (a kite also has them); equal bisecting diagonals give a rectangle, not necessarily a square.

Frequently Asked Questions

What is the sum of the interior angles of any quadrilateral?
The sum of the interior angles of any quadrilateral is always 360 degrees, regardless of its specific shape, because a quadrilateral can be divided into two triangles, each contributing 180 degrees.

Last Updated: September 23, 2026

What distinguishes a parallelogram from a general quadrilateral?
A parallelogram is a special quadrilateral in which both pairs of opposite sides are parallel and equal in length, and its opposite angles are also equal, properties a general quadrilateral does not necessarily have.

Written by Satish

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