NCERT Exemplar Solutions
Class 6 - Mathematics

Unit 9: Symmetry and Practical Geometry

The distance of the image of a point (or an object) from the line of symmetry (mirror) is _____ as that of the point (object) from the line (mirror).

The number of lines of symmetry in a picture of Taj Mahal is ____.

The number of lines of symmetry in a rectangle and a rhombus are _____ (equal/unequal).

The number of lines of symmetry in a rectangle and a square are _____ (equal/unequal).

If a line segment of length 5 cm is reflected in a line of symmetry (mirror), then its reflection (image) is a _____ of length _____.

If an angle of measure \(80^\circ\) is reflected in a line of symmetry, then the reflection is an _____ of measure _____.

The image of a point lying on a line \(l\) with respect to the line of symmetry \(l\) lies on _____.

In Fig. 9.10, if B is the image of the point A with respect to the line \(l\) and P is any point lying on \(l\), then the lengths of line segments PA and PB are _____.

The number of lines of symmetry in Fig. 9.11 is ____.

The common properties in the two set-squares of a geometry box are that they have a _____ angle and they are of the shape of a _____.

The digits having only two lines of symmetry are _____ and _____.

The digit having only one line of symmetry is ____.

The number of digits having no line of symmetry is ____.

The number of capital letters of the English alphabets having only vertical line of symmetry is ____.

The number of capital letters of the English alphabets having only horizontal line of symmetry is ____.

The number of capital letters of the English alphabets having both horizontal and vertical lines of symmetry is ____.

The number of capital letters of the English alphabets having no line of symmetry is ____.

The line of symmetry of a line segment is the _____ bisector of the line segment.

The number of lines of symmetry in a regular hexagon is ____.

The number of lines of symmetry in a regular polygon of \(n\) sides is ____.

A protractor has _____ line/lines of symmetry.

A \(30^\circ\)–\(60^\circ\)–\(90^\circ\) set-square has _____ line/lines of symmetry.

A \(45^\circ\)–\(45^\circ\)–\(90^\circ\) set-square has _____ line/lines of symmetry.

A rhombus is symmetrical about _____.

A rectangle is symmetrical about the lines joining the _____ of the opposite sides.

A right triangle can have at most one line of symmetry.

A kite has two lines of symmetry.

A parallelogram has no line of symmetry.

If an isosceles triangle has more than one line of symmetry, then it need not be an equilateral triangle.

If a rectangle has more than two lines of symmetry, then it must be a square.

With ruler and compasses, we can bisect any given line segment.

Only one perpendicular bisector can be drawn to a given line segment.

Two perpendiculars can be drawn to a given line from a point not lying on it.

With a given centre and a given radius, only one circle can be drawn.

Using only the two set-squares of the geometry box, an angle of 40° can be drawn.

Using only the two set-squares of the geometry box, an angle of 15° can be drawn.

If an isosceles triangle has more than one line of symmetry, then it must be an equilateral triangle.

A square and a rectangle have the same number of lines of symmetry.

A circle has only 16 lines of symmetry.

A 45°-45°-90° set-square and a protractor have the same number of lines of symmetry.

It is possible to draw two bisectors of a given angle.

A regular octagon has 10 lines of symmetry.

Infinitely many perpendiculars can be drawn to a given ray.

Infinitely many perpendicular bisectors can be drawn to a given ray.

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.