NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry

Problems and Solutions

Is there any line of symmetry in the Fig. 9.12? If yes, draw all the lines of symmetry.

In Fig. 9.13, PQRS is a rectangle. State the lines of symmetry of the rectangle.

Write all the capital letters of the English alphabets which have more than one lines of symmetry.

Write the letters of the word ‘MATHEMATICS’ which have no line of symmetry.

Write the number of lines of symmetry in each letter of the word ‘SYMMETRY’.

Match the following:

Open your geometry box. There are some drawing tools. Observe them and complete the following table:

Draw the images of points A and B in line l of Fig. 9.14 and name them as A′ and B′ respectively. Measure AB and A′B′. Are they equal?

In Fig. 9.15, the point C is the image of point A in line l and line segment BC intersects the line l at P.

(a) Is the image of P in line l the point P itself?
(b) Is PA = PC?
(c) Is PA + PB = PC + PB?
(d) Is P that point on line l from which the sum of the distances of points A and B is minimum?

Complete the figure so that line l becomes the line of symmetry of the whole figure (Fig. 9.16).

Draw the images of the points A, B and C in the line m (Fig. 9.17). Name them as A′, B′ and C′, respectively and join them in pairs. Measure AB, BC, CA, A′B′, B′C′ and C′A′. Is AB = A′B′, BC = B′C′ and CA = C′A′?

Draw the images P′, Q′ and R′ of the points P, Q and R, respectively in the line n (Fig. 9.18). Join P′Q′ and Q′R′ to form an angle P′Q′R′. Measure ∠PQR and ∠P′Q′R′. Are the two angles equal?

Complete Fig. 9.19 by taking l as the line of symmetry of the whole figure.

Draw a line segment of length 7 cm. Draw its perpendicular bisector, using ruler and compasses.

Draw a line segment of length 6.5 cm and divide it into four equal parts, using ruler and compasses.

Draw an angle of 140° with the help of a protractor and bisect it using ruler and compasses.

Draw an angle of 65° and draw an angle equal to this angle, using ruler and compasses.

Draw an angle of 80° using a protractor and divide it into four equal parts, using ruler and compasses. Check your construction by measurement.

Copy Fig. 9.20 on your notebook and draw a perpendicular to l through P, using (i) set squares (ii) protractor (iii) ruler and compasses. How many such perpendiculars are you able to draw?

Copy Fig. 9.21 on your notebook and draw a perpendicular from P to line m, using (i) set squares (ii) Protractor (iii) ruler and compasses. How many such perpendiculars are you able to draw?

Draw a circle of radius 6 cm using ruler and compasses. Draw one of its diameters. Draw the perpendicular bisector of this diameter. Does this perpendicular bisector contain another diameter of the circle?

Bisect ∠XYZ of Fig. 9.22

Draw an angle of 60° using ruler and compasses and divide it into four equal parts. Measure each part.

Bisect a straight angle, using ruler and compasses. Measure each part.

Bisect a right angle, using ruler and compasses. Measure each part. Bisect each of these parts. What will be the measure of each of these parts?

Draw an angle ABC of measure 45°, using ruler and compasses. Now draw an angle DBA of measure 30°, using ruler and compasses as shown in Fig. 9.23. What is the measure of ∠DBC?

Draw a line segment of length 6 cm. Construct its perpendicular bisector. Measure the two parts of the line segment.

Draw a line segment of length 10 cm. Divide it into four equal parts. Measure each of these parts.