NCERT Solutions for Class 8th Maths Chapter 4 Quadrilaterals
Updated on 2026-09-19
About this chapter
A rectangle can be defined in three equivalent ways — all angles 90°; all angles 90° with opposite sides equal; or diagonals equal and bisecting each other. The chapter proves that these describe exactly the same set of quadrilaterals. Congruence does the heavy lifting. SAS, AAS, ASA and SSS are used in Deductions 1–10 to establish every side, angle and diagonal property in the chapter. The angle sum of any quadrilateral is 360°, because one diagonal splits it into two triangles. This is why three right angles force the fourth to be a right angle too. Parallelogram: opposite sides parallel ⇒ opposite sides equal, opposite angles equal, adjacent angles supplementary, diagonals bisect each other. A rhombus adds equal sides; the diagonals then also become perpendicular and bisect the angles.
- Introduction
- .1 Rectangles and Squares
- .1 A Special Rectangle
- .2 Angles in a Quadrilateral
- .3 More Quadrilaterals with Parallel Opposite Sides
- .4 Quadrilaterals with Equal Sidelengths
- .5 Playing with Quadrilaterals
- .6 Kite and Trapezium
- Puzzle Time
Quick revision
| Quadrilateral | Definition used in the book | Sides and angles | Diagonals |
|---|---|---|---|
| Rectangle | All four angles are 90° | Opposite sides equal and parallel | Equal; bisect each other |
| Square | All angles 90° and all sides equal | All sides equal, opposite sides parallel | Equal; bisect each other at 90°; bisect the angles |
| Parallelogram | Opposite sides are parallel | Opposite sides equal; opposite angles equal; adjacent angles add to 180° | Bisect each other (need not be equal) |
| Rhombus | All four sides are equal | Opposite sides parallel; opposite angles equal; adjacent angles add to 180° | Bisect each other at 90°; bisect the angles (need not be equal) |
| Kite | Can be labelled ABCD with AB = BC and CD = DA | Two adjacent pairs of equal sides; one pair of opposite angles equal | One diagonal bisects the other at 90° and bisects two angles |
| Trapezium | At least one pair of parallel opposite sides | Angles on the same leg add to 180° | No special property |
| Isosceles trapezium | Trapezium whose non-parallel sides are equal | Angles on each parallel side are equal | Equal in length |
| Any quadrilateral | Closed figure with four sides | Angle sum is 360° | A diagonal splits it into two triangles |
Exercises
- Introduction — In-text Questions Page 82
- .1 Rectangles and Squares — In-text Questions Page 83–854
- .1 Rectangles and Squares — In-text Questions Page 86–874
- .1 Rectangles and Squares — In-text Questions Page 89–904
- .1 A Special Rectangle — In-text Questions Page 90–934
- .1 Rectangles and Squares — Figure it Out Page 944
- .2 Angles in a Quadrilateral — In-text Questions Page 94–954
- .3 More Quadrilaterals with Parallel Opposite Sides — In-text Questions Page 95–994
- .4 Quadrilaterals with Equal Sidelengths — In-text Questions Page 99–1024
- .4 Quadrilaterals with Equal Sidelengths — Figure it Out Page 1024
- .5 Playing with Quadrilaterals — Geoboard Activity Page 1034
- .5 Playing with Quadrilaterals — Joining Triangles Page 104–1054
- .6 Kite and Trapezium — In-text Questions Page 105–1074
- .6 Kite and Trapezium — Figure it Out Page 107–1094
- Puzzle Time — Which Quad? Page 111