Chapter 4 — Quadrilaterals

Chapter 4 of the Class 8 Maths NCERT textbook (Ganita Prakash), "Quadrilaterals", teaches four-sided figures and their properties through geometric reasoning. It covers rectangles, squares, parallelograms, rhombuses, kites, and trapeziums, with emphasis on proofs using congruence, angle sums, and diagonal properties.

• Discovering properties by reasoning — Rather than memorising, students deduce quadrilateral properties — starting from the fact that any quadrilateral's angles sum to 360° — using congruence and angle relationships to justify each result.
• Diagonals define the family — How the diagonals behave (equal, bisecting, perpendicular) distinguishes rectangles, squares, rhombuses and kites from each other, making diagonals the key to classifying special quadrilaterals.
• From geometry to construction — The reasoning feeds practical work such as the carpenter's method of building a true rectangle using equal, mutually bisecting diagonals — linking abstract proof to real construction.

1. 01The sum of all angles in any quadrilateral is always 360°
2. 02A rectangle is a quadrilateral with all 90° angles; its diagonals are equal in length and bisect each other
3. 03A square is a special rectangle where all sides are equal and diagonals bisect each other at right angles (90°)
4. 04A parallelogram has opposite sides parallel and equal, opposite angles equal, and diagonals that bisect each other
5. 05A rhombus has all four sides equal, opposite angles equal, and diagonals that bisect each other at 90° and bisect the angles
6. 06A trapezium has at least one pair of parallel opposite sides; an isosceles trapezium has equal non-parallel sides
7. 07A kite has two pairs of adjacent equal sides and diagonals where one bisects the other at right angles