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Playing with Constructions – Class 6 Mathematics notes, important questions and MCQs

NCERT Class 6 Mathematics, chapter 8. Notes, key terms, important questions with answers and MCQs.

Chapter overview

A ruler and a compass let us draw exact figures. A compass draws circles and marks points at a fixed distance from a point. Using them we construct squares and rectangles, study their diagonals and find points that are equally far from two given points.

Circles and fixed distances

A circle is the set of all points at the same distance (the radius) from a fixed point (the centre).
To mark a point at a given distance from point A, open the compass to that length, put its tip on A and draw an arc.
Two circles of radius r drawn from points that are less than 2r apart cross at two points.

Squares and rectangles

A rectangle has opposite sides equal and all four angles equal to 90°.
A square has all four sides equal and all four angles equal to 90°; every square is a rectangle, but not every rectangle is a square.
To construct a rectangle of given length and breadth, draw one side, draw perpendiculars at both ends, mark the breadth on them with the compass and join the top points.

Diagonals and equidistant points

The two diagonals of a rectangle are equal and cut each other into two equal halves.
The diagonals of a square are equal, bisect each other and meet at 90°.
All points equidistant from two points A and B lie on the perpendicular bisector of the segment AB.

Key terms

Radius: the fixed distance from the centre of a circle to any point on it
Diagonal: a line segment joining two opposite corners of a quadrilateral
Perpendicular: a line that meets another line at a right angle (90°)
Equidistant: at the same distance from two or more points

Formulas

Rectangle: opposite sides equal, each angle 90°
Square: all sides equal, each angle 90°

Important questions with answers

What is the difference between a square and a rectangle?2 marks

Both have all angles equal to 90°. In a rectangle only the opposite sides are equal, while in a square all four sides are equal. So every square is a rectangle, but a rectangle is a square only when its length equals its breadth.

Write the steps to construct a rectangle of length 7 cm and breadth 4 cm.3 marks

Draw AB = 7 cm. At A and B draw lines perpendicular to AB using a protractor or compass. With the compass set to 4 cm, cut these lines at D and C from A and B. Join DC. ABCD is the required rectangle; check that DC = 7 cm and that the diagonals AC and BD are equal.

State the properties of the diagonals of a rectangle and a square, and explain how to find all points equidistant from two given points A and B.5 marks

In a rectangle, the two diagonals are equal in length and bisect each other, so the point where they meet is the same distance from all four corners. In a square, the diagonals are equal, bisect each other and are also perpendicular, so they divide the square into four identical right-angled triangles. To find points equidistant from A and B, open the compass to more than half of AB and draw arcs from A and from B so that they cross above and below AB. Every crossing point is the same distance from A and B. The line through these crossing points is the perpendicular bisector of AB, and every point on it is equidistant from A and B.

Quick revision

Compass = circles and fixed distances.
Square: equal sides; rectangle: equal opposite sides; both have 90° angles.
Rectangle diagonals: equal and bisect each other.
Equidistant points lie on the perpendicular bisector.

Exam tips

Keep the compass width fixed while drawing both arcs; changing it spoils the construction.
Check a constructed rectangle by measuring both diagonals; they must be equal.

Practice MCQs

All the points on a circle are at the same distance from
1. the centre
2. any point outside
3. the diameter's end
4. the ruler
Show answer
Answer: (a) the centre. This distance is the radius.
Each angle of a rectangle measures
1. 45°
2. 60°
3. 90°
4. 180°
Show answer
Answer: (c) 90°. All four angles are right angles.
A quadrilateral with all sides equal and all angles 90° is a
1. rhombus only
2. square
3. rectangle only
4. trapezium
Show answer
Answer: (b) square. It satisfies both conditions.
The diagonals of a rectangle are
1. always unequal
2. perpendicular always
3. equal and bisect each other
4. parallel
Show answer
Answer: (c) equal and bisect each other. They are equal in length and cut each other into halves.
A rectangle has length 6 cm and breadth 4 cm. Its perimeter is
1. 10 cm
2. 20 cm
3. 24 cm
4. 48 cm
Show answer
Answer: (b) 20 cm. 2 × (6 + 4) = 20 cm.
To mark a point exactly 5 cm from point P, you should
1. guess with a ruler
2. open the compass to 5 cm and draw an arc from P
3. draw a circle of 10 cm
4. use a protractor
Show answer
Answer: (b) open the compass to 5 cm and draw an arc from P. Every point on that arc is 5 cm from P.
Points that are equally distant from points A and B lie on
1. the line AB only
2. a line parallel to AB through A
3. a circle with diameter AB
4. the perpendicular bisector of AB
Show answer
Answer: (d) the perpendicular bisector of AB. Every point on the perpendicular bisector is equidistant from A and B.
Which property is true for a square but not for every rectangle
1. diagonals are equal
2. diagonals bisect each other
3. all angles are 90°
4. diagonals are perpendicular
Show answer
Answer: (d) diagonals are perpendicular. In a square the diagonals meet at 90°.

All chapters of Class 6 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.