Summary
Chapter 8 'Playing with Constructions' of Class 6 Ganita Prakash teaches students to draw circles, squares, and rectangles accurately using a ruler and compass, and explores the properties of these shapes including diagonals and equidistant points.
This chapter introduces geometric construction tools — a ruler and compass — and uses them to draw circles, squares, and rectangles. Students learn the defining properties of rectangles (opposite sides equal, all angles 90°) and squares (all sides equal, all angles 90°), and then construct these figures step by step. The chapter also explores creative artwork (Wavy Wave, House, Eyes) built from circles and arcs, investigates how the diagonals of rectangles and squares behave, and develops the concept of finding a point equidistant from two given points using intersecting arcs.
Key points & formulas
- 01A circle is the set of all points at a fixed distance (the radius) from a centre point; a compass draws this by keeping the needle fixed and rotating the pencil.
- 02Any shape drawable on paper with a pencil is called a curve in NCERT — this includes straight lines, circles, and arcs.
- 03Rectangle property R1: opposite sides are equal. Property R2: all four angles are 90°.
- 04Square property S1: all four sides are equal. Property S2: all four angles are 90°. Every square satisfies rectangle properties too.
- 05A rectangle or square named with corner labels must list corners in order of travel (clockwise or anticlockwise) around the figure; random orderings like ABDC are invalid.
- 06Rotating a square produces another square — rotation does not change side lengths or angles.
- 07A rectangle can be divided into n identical squares when its longer side equals n times its shorter side (e.g., 3 identical squares: length = 3 × breadth).
- 08To construct a rectangle given one side and a diagonal: draw the side, erect a perpendicular at one end, then draw a circle of radius equal to the diagonal from the opposite end — the intersection gives the third vertex.
- 09The two diagonals of a rectangle are equal in length; in a square each diagonal also bisects the corner angles into two equal 45° parts.
- 10A point equidistant from two fixed points B and C is found by drawing arcs of equal radius from B and C — their intersection is the required point (used in the 'House' construction).
Frequently asked questions
01What is Chapter 8 'Playing with Constructions' about in Class 6 Maths?
It teaches geometric constructions using a ruler and compass: drawing circles, squares, and rectangles; understanding their properties (angles, sides, diagonals); and creating artwork like a Wavy Wave, a Person, Eyes, and a House using arcs and straight lines.
02What are the two instruments used in this chapter for constructions?
A ruler and a compass. The compass is used to draw circles and arcs (by fixing the needle and rotating the pencil), and the ruler is used to draw straight lines and set the compass radius.
03What is a curve according to Class 6 Ganita Prakash Chapter 8?
Any shape that can be drawn on paper with a pencil, including straight lines, circles, and all other figures — not just wavy or bent shapes.
04What are the two properties of a rectangle stated in this chapter?
R1: Opposite sides are equal in length. R2: All four angles are 90°. Both properties must be satisfied for a figure to be a rectangle.
05How is a square different from a rectangle in this chapter?
A square has all four sides equal (S1) and all four angles 90° (S2). A rectangle only requires opposite sides to be equal. Every square is a rectangle, but not every rectangle is a square.
06What happens to a square when it is rotated?
It remains a square. Rotating does not change side lengths or angles, so the rotated figure still satisfies both square properties S1 and S2.
07How do you construct a rectangle when one side and the diagonal are given?
Draw the given side (e.g., CD = 5 cm). Erect a perpendicular at one end (C). Then draw a circle of radius equal to the diagonal (7 cm) centred at the other end (D). Where this circle crosses the perpendicular is the third vertex (B). Complete the rectangle using perpendiculars or a compass transfer.
08What is the radius and what is AX in the Wavy Wave construction when AB = 8 cm?
The radius for each half-circle is 2 cm, and AX = 4 cm. Each half-circle spans a diameter of 4 cm along the central line, so two half-circles fill the full 8 cm line AB.
09How do you find a point that is equidistant from two given points using a compass?
Draw arcs of equal radius from each of the two given points. Where the arcs intersect is a point equidistant from both. This technique is used in the House construction to find the apex A that is 5 cm from both B and C.
10What do the diagonals of a rectangle look like, and what is special about them in a square?
A rectangle has two diagonals that are equal in length. In a square, the diagonals are also equal and additionally each diagonal splits every 90° corner angle into two equal 45° angles.
11Can a 4-sided figure have all angles equal to 90° but opposite sides not equal?
No. The chapter confirms this is impossible — whenever all four angles of a quadrilateral are 90°, opposite sides must be equal, making it a rectangle.
12Is the Ganita Prakash Class 6 Chapter 8 PDF available free without sign-up?
Yes. The official NCERT PDF of Ganita Prakash Class 6 (including Chapter 8 Playing with Constructions) is available for free download on cbseprepmaster.com with no sign-up required.
More chapters in Ganita Prakash
This is the complete Ganita Prakash Chapter 8 as published by NCERT — every diagram, solved example, and exercise included, free. Browse all NCERT Class 6 textbooks.
Read offline with notes, solutions & mock tests
CBSE Prepmaster — free on iOS & Android