NCERT Class 6 Maths Chapter 8 – Playing with Constructions (Ganita Prakash) | Complete Explanation with Step-by-Step Solutions

NCERT Class 6 Maths Chapter 8 – Playing with Constructions

Ganita Prakash | Complete Guide with Solutions

Geometry becomes interesting when we start constructing shapes using mathematical tools like ruler and compass.

In Chapter 8 – Playing with Constructions, students learn how to draw geometric figures accurately and understand important properties of shapes like circles, squares, rectangles and diagonals.

This chapter develops spatial thinking and introduces the concept of geometric construction, which is a fundamental topic in mathematics.

In this blog, we will cover:

• Introduction to constructions
• Important definitions
• Step-by-step geometric constructions
• Solved NCERT questions
• Concept explanations for better understanding

1. Introduction to Geometric Constructions

Geometric construction means drawing shapes using mathematical instruments such as ruler and compass.

These constructions help us draw accurate shapes instead of rough sketches.

For example:

• Drawing a circle with a fixed radius
• Constructing squares and rectangles
• Finding points at equal distance

These skills help students understand geometry visually and logically.

2. Important Terms and Definitions

Curve

Any shape that can be drawn continuously without lifting the pencil.

Examples:

• Straight line

• Circle

• Curved figures

Circle

A circle is the set of all points that are at the same distance from a fixed point.

That fixed point is called the centre.

Centre

The fixed point inside the circle from which every point on the circle is at the same distance.

Radius

The distance between the centre and any point on the circle.

3. Constructing a Circle Using Compass

Steps:

1. Mark a point P on paper.

2. Open the compass to 4 cm using a ruler.

3. Place the needle on point P.

4. Rotate the compass pencil around the point.

Result:

You get a circle of radius 4 cm.

Important Observation:

All points on the circle are exactly 4 cm away from P.

4. Section 8.1 – Artwork

In this section, students learn how to create artistic designs using a ruler and compass.

Examples:

Wavy wave

Person figure

Eyes

These activities help improve precision and creativity.

Example Question

What radius should be taken in the compass to draw the half circle in the wave?

Solution

Radius = 2 cm

Length of AX = 4 cm

This produces the required half circle wave.

5. Squares and Rectangles

Rectangle

A rectangle has the following properties:

1. Opposite sides are equal

2. All angles are 90°

Example:

AB = CD
BC = AD

Square

A square satisfies:

1. All sides equal

2. All angles = 90°

Important Concept

Even if a square or rectangle is rotated, it still remains the same shape because:

• Side lengths remain equal
• Angles remain 90°

Question

Which of the following is not a valid name for the square?

1 PQSR
2 SPQR
3 RSPQ
4 QRSP

Solution

Correct Answer:

PQSR

Reason:

Names must follow the order of vertices around the figure.

6. Constructing Squares

Example

Construct a square of side 6 cm

Steps

Step 1
Draw line segment PQ = 6 cm

Step 2
Draw a perpendicular at point P

Step 3
Mark point S such that PS = 6 cm

Step 4
Draw perpendicular at Q

Step 5
Join the remaining sides

Result:

Square PQRS

All sides = 6 cm

All angles = 90°

7. Constructing Rectangles

Question

Draw a rectangle with sides 4 cm and 6 cm

Solution

Step 1
Draw AB = 6 cm

Step 2
Draw a perpendicular at A

Step 3
Mark AD = 4 cm

Step 4
Draw a perpendicular at B

Step 5
Join points to complete rectangle

Verification:

Angle A = Angle B = Angle C = Angle D = 90°

Opposite sides are equal.

8. Diagonals of a Rectangle

In rectangle PQRS

Two diagonals are:

PR
QS

Important observation:

Diagonals of a rectangle are equal in length.

They divide the rectangle into triangles.

9. Constructing Rectangle with Diagonal

Example

Construct a rectangle where:

Side = 5 cm
Diagonal = 7 cm

Steps

Step 1
Draw DC = 5 cm

Step 2
Draw a perpendicular line at point C

Step 3
With D as centre, draw a circle with radius 7 cm

Step 4
The intersection point gives point B

Step 5
Complete rectangle ABCD

10. Points Equidistant from Two Points

If a point is equally distant from two points, it lies on the intersection of two circles drawn from those points.

Example:

To locate point A

• Draw a circle from B radius 5 cm
• Draw another circle from C radius 5 cm

The intersection gives point A.

11. Interesting Construction – House

All sides are 5 cm.

Steps:

1 Draw base BC
2 Draw circles from B and C with radius 5 cm
3 Intersection gives point A
4 Complete the figure using arcs

This activity teaches intersection of circles in construction.

Key Learning Summary

After completing Chapter 8 students learn:

• How to draw circles using compass
• Properties of squares and rectangles
• Construction of geometric shapes
• Concept of diagonals
• Points equidistant from two points

These concepts build the foundation for advanced geometry in higher classes.

Practice Questions for Students

1 Construct a square of side 7 cm.
2 Draw a rectangle of sides 8 cm and 5 cm.
3 Construct a rectangle whose side = 4 cm and diagonal = 8 cm.
4 Draw a figure where all sides are equal but it is not a square.

Final Words

Chapter Playing with Constructions is one of the most practical and visual chapters in Class 6 Maths.

Students should practice these constructions using compass and ruler to understand geometry deeply.

Consistent practice will improve accuracy, logical thinking, and diagram skills.

For more clear explanations and solved questions, keep visiting

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Previous Chapter: Chapter 7 – Fractions
Next Chapter: Chapter 9 – Symmetry