Chapter 4 — Quadrilaterals

Chapter 4 of Class 8 maths, "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.

This chapter explores quadrilaterals—four-sided figures—by discovering their defining properties through geometric deduction. Students learn that all quadrilateral angles sum to 360°, investigate how diagonals determine special quadrilaterals (rectangles have equal diagonals that bisect each other; squares have perpendicular bisecting diagonals), and classify quadrilaterals by their parallel sides (parallelograms, trapeziums) and equal side lengths (rhombuses, kites). Practical applications include the carpenter's method for constructing rectangles using equal, bisecting diagonals.

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