NCERT Solutions for Class 6th Maths Chapter 8 Playing with Constructions
Updated on 2026-09-19
About this chapter
A circle is the set of all points at the same distance from one fixed point. That point is the centre and the fixed distance is the radius . This is why a compass — which keeps its opening fixed — draws circles and arcs. A rectangle obeys two rules: R1 opposite sides are equal, R2 all four angles are 90°. A square obeys S1 all sides equal and S2 all angles 90°. Turning (rotating) a figure changes neither its sides nor its angles, so a rotated square is still a square. A figure is named by travelling around its boundary — ABCD, BCDA, DCBA are all valid names of the same rectangle, but ABDC is not. The best way to construct a figure is to draw a rough diagram first , mark on it everything you know, and then decide the order in which the points can be located. A rectangle can be constructed w
- Artwork
- Squares and Rectangles
- Constructing Squares and Rectangles
- An Exploration in Rectangles
- squares inside squares and rectangles
- Exploring Diagonals of Rectangles and Squares
- rectangles from an angle or a diagonal
- Points Equidistant from Two Given Points
- Hints A) Eyes and B) the four equal sides
Quick revision
| Idea | Rule in short | Example from the chapter | Result |
|---|---|---|---|
| Circle | all points at the same distance from the centre | centre P, radius 4 cm | every point of the circle is 4 cm from P |
| Compass | keeps one opening fixed while the pencil turns | opened to 4 cm against a ruler | a circle or an arc of radius 4 cm |
| Rectangle | R1 opposite sides equal, R2 all angles 90° | ABCD with AB = 7 cm, BC = 4 cm | DC = 7 cm, AD = 4 cm |
| Square | S1 all sides equal, S2 all angles 90° | PQRS of side 6 cm | RS = 6 cm, ∠R = ∠S = 90° |
| Valid name | corners taken in order of travel | PQSR for the square PQRS | not a valid name |
| Rotated figure | turning changes no length and no angle | a square turned like a diamond | still a square |
| Rectangle from two sides | side → perpendicular → side → perpendicular | sides 4 cm and 6 cm | rectangle 4 cm × 6 cm |
| Rectangle from side + diagonal | arc of radius = diagonal cuts the perpendicular | side 5 cm, diagonal 7 cm | other side ≈ 4.9 cm |
| Diagonals of a rectangle | always equal in length | rectangle 7 cm × 4 cm | both diagonals ≈ 8.1 cm |
| Diagonal and the corner angle | splits 90° into two unequal parts | 60° + 30° at A | equal parts (45° + 45°) only in a square |
| Rectangle into identical squares | long side = 2 × (or 3 ×) the short side | AF = 4 cm | AC = 8 cm (two squares), 12 cm (three) |
| Point at given distances from two points | cross two arcs | 5 cm from B and 5 cm from C | the apex A of the house |
Exercises
- In-text Questions — Artwork Page 188 & 189
- Construct — Artwork Page 190 & 191
- Figure it Out — Artwork Page 191
- Construct — Artwork Page 192
- In-text Questions — Squares and Rectangles Page 193
- Figure it Out — Squares and Rectangles Page 194
- In-text Questions — Constructing Squares and Rectangles Page 195 & 196
- Construct — Constructing Squares and Rectangles Page 197
- In-text Questions — An Exploration in Rectangles Page 197 – 199
- Construct: Breaking Rectangles — An Exploration in Rectangles Page 199 – 201
- Construct — squares inside squares and rectangles Page 201 – 203
- In-text Questions — Exploring Diagonals of Rectangles and Squares Page 203 & 204
- Construct — rectangles from an angle or a diagonal Page 205 – 210
- Construct — Exploring Diagonals of Rectangles and Squares Page 211
- Construct: House — Points Equidistant from Two Given Points Page 211 – 214
- Construct — Points Equidistant from Two Given Points Page 215
- Hints A) Eyes and B) the four equal sides — Hints Page 215 & 216