NCERT Exemplar Class 6 Maths Symmetry and Practical Geometry Solution

In questions 1 to 17, out of the given four options, only one is correct. Write the correct answer.

Question 1:

In the following figures, the figure that is not symmetric with respect to any line is:

(A) (i)

(B) (ii)

(C) (iii)

(D) (iv)

Solution:

is not symmetric any line.

Question 2:

The number of lines of symmetry in a scalene triangle is
(A) 0

(B) 1

(C) 2

(D) 3

Solution: Answers is A.

The number of lines of symmetry in a scalene triangle there is number line symmetry.

Question 3:

The number of lines of symmetry in a circle is
(A) 0
(B) 2
(C) 4
(D) more than 4

Solution: Answer is D.

The number of lines of symmetry in a circle is more than.

Question 4:

Which of the following letters does not have the vertical line of
symmetry?
(A) M

(B) H

(C) E

(D) V

Solution: Answer is C.

In letter E does not have the vertical line of symmetry.

Question 5:

Which of the following letters have both horizontal and vertical lines
of symmetry?
(A) X

(B) E

(C) M

(D) K

Solution: Answer is A.

In letter X have both horizontal and vertical line of symmetry.

Question 6:

Which of the following letters does not have any line of symmetry?
(A) M

(B) S

(C) K

(D) H

Solution: Answer is B.

In letter s does not have any line of symmetry.

Question 7:

Which of the following letters has only one line of symmetry?

(A) H

(B) X

(C) Z

(D) T

Solution: Answer is D.

Letter T has only one line of symmetry.

Question 8:

The instrument to measure an angle is a

(A) Ruler

(B) Protractor

(C) Divider

(D) Compasses

Solution: Answer is B.

The instrument to measure an angle is protractor.

Question 9:

The instrument to draw a circle is

(A) Ruler

(B) Protractor

(C) Divider

(D) Compasses

Solution: Answer is B.

The instrument to draw a circle is Protractor.

Question 10:

Number of set squares in the geometry box is

(A) 0

(B) 1

(C) 2

(D) 3

Solution: Answer is C.

2 Is the number of sets of squares in the geometry box.

Question 11:

The number of lines of symmetry in a ruler is

(A) 0

(B) 1

(C) 2

(D) 4

Solution: Answers is C.

2 is the number of lines of symmetry in a ruler.

Question 12:

The number of lines of symmetry in a divider is

(A) 0

(B) 1

(C) 2

(D) 3

Solution: Answer is B.

The number of lines of symmetry in a divider is 2.

Question 13:

The number of lines of symmetry in compasses is

(A) 0

(B) 1

(C) 2

(D) 3

Solution: Answers is A.

The number of lines of symmetry in compasses is 0.

There is number line of symmetry in compasses.

Question 14:

The number of lines of symmetry in a protractor is

(A) 0

(B) 1

(C) 2

(D) more than 2

Solution: Answer is B.

The number of lines of symmetry in a protractor is 1.

Question 15:

The number of lines of symmetry in a 45° – 45° – 90° set-square is

(A) 0

(B) 1

(C) 2

(D) 3

Solution: Answer is A.

The number of lines of symmetry in a 45°- 45° – 90° set-square is 1.

Question 16:

The number of lines of symmetry in a 30° – 60° – 90° set square is

(A) 0

(B) 1

(C) 2

(D) 3

Solution: Answers is A.

There is number line of symmetry in 30° – 60° – 90° set square.

Question 17:

The instrument in the geometry box having the shape of a triangle is called a

(A) Protractor

(B) Compasses

(C) Divider

(D) Set-square

Solution: Answers is D.

The instrument in the geometry box having the shape of a triangle is called a Set-square.

In questions 18 to 42, fill in the blanks to make the statements true.

Question 18:

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).

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

Question 19:

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

Solution: The number of lines of symmetry in a picture of Taj Mahal is one.

Question 20:

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

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

Question 21:

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

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

Question 22:

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

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

Question 23:

If an angle of measure 80o is reflected in a line of symmetry, then the reflection is an ______ of measure _______.

Solution: If an angle of measure 80° is reflected in a line of symmetry, then the reflection is an Angle of measure 80°.

Question 24:

The image of a point lying on a line l with respect to the line of symmetry l lies on _______.

Solution: The image of a point lying on a line l with respect to the line of symmetry l lies on l.

Question 25:

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 _______.

Solution:

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 equal.

Question 26:

The number of lines of symmetry in Fig. 9.11 is__________.

Solution: The number of lines of symmetry in Fig. 9.11 is 4.

Question 27:

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 ______.

Solution:

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

Question 28:

The digits having only two lines of symmetry are ______ and _______.

Solution: The digits having only two lines of symmetry are 0 and 8.

Question 29:

The digit having only one line of symmetry is _______.

Solution: The digit having only one line of symmetry is 3.

Question 30:

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

Solution: The number of digits having no line of symmetry is 7 (1, 2, 4, 5, 6, 7, 9).

Question 31:

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

Solution: The number of capital letters of the English alphabets having only vertical line of symmetry is 7 ( A, M, U, V, W, Y, T).

Question 32:

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

Solution: The number of capital letters of the English alphabets having only vertical line of symmetry is 5 (B, C, D, E, K).

Question 33:

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

Solution: The number of capital letters of the English alphabets having both horizontal and vertical lines of symmetry is 5 (B, C, D, E, K).

Question 34:

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

Solution: The number of capital letters of the English alphabets having no line of symmetry is 10 (F, G, J, L, N, P, Q, R, S, Z).

Question 35:

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

Solution: The line of symmetry of a line segment is the perpendicular bisector of the line segment.

Question 36:

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

Solution: The number of lines of symmetry in a regular hexagon is 6.

Question 37:

The number of lines of symmetry in a regular polygon of n sides is ______.

Solution: The number of lines of symmetry in a regular polygon of n sides is n.

Question 38:

A protractor has _______ line/lines of symmetry.

Solution: A protractor has one line/lines of symmetry.

Question 39:

A 30° – 60° – 90° set-square has ________ line/lines of symmetry.

Solution: A 30° – 60° – 90° set-square has no line/lines of symmetry.

Question 40:

A 45° – 45° – 90° set-square has _______ line/lines of symmetry.

Solution: A 45° – 45° – 90° set-square has one line/lines of symmetry.

Question 41:

A rhombus is symmetrical about _______.

Solution: A rhombus is symmetrical about diagonals.

Question 42:

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

Solution: A rectangle is symmetrical about the lines joining the mid points of the opposite sides.

In questions 43 – 61, state whether the statements are true (T) or false (F).

Question 43:

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

Solution: The statement true.

Question 44:

A kite has two lines of symmetry.

Solution: False.

A kite has not two lines of symmetry.

Question 45:

A parallelogram has no line of symmetry.

Solution: The statement true.

Question 46:

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

Solution: False

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

Question 47:

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

Solution: The statement true.

Question 48:

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

Solution: The statement true.

Question 49:

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

Solution: The statement true.

Question 50:

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

Solution: False

Two perpendiculars can be drawn to a given line from a point lying on it.

Question 51:

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

Solution: The statement true.

Question 52:

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

Solution: False

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

Question 53:

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

Solution: The statement true.

Question 54:

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

Solution: The statement true.

Question 55:

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

Solution: False

A square and a rectangle have not the same number of lines of symmetry.

Question 56:

A circle has only 16 lines of symmetry.

Solution: False

A circle has only many lines of symmetry.

Question 57:

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

Solution: The statement true.

Question 58:

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

Solution: False

It is not possible to draw two bisectors of a given angle.

Question 59:

A regular octagon has 10 lines of symmetry.

Solution: False

A regular octagon has 8 lines of symmetry.

Question 60:

Infinitely many perpendiculars can be drawn to a given ray.

Solution: The statement true.

Question 61:

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

Solution: False

Infinitely many perpendicular bisectors can’t be drawn to a given ray.

Question 62:

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

Solution: Yes, there is one line of symmetry in the fig 9.12

Question 63:

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

Solution: BD and AC is the line of symmetry of the rectangle PQRS.

Question 64:

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

Solution: O, X, J, H these are the capital letter of the alphabets which have more than one line of symmetry.

Question 65:

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

Solution: From the word ‘MATHEMATICS’ there is only S aphanite’s which have number line of symmetry.

Question 66:

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

Solution: S and R has zero means number line of symmetry.

Y, M, T, E has only one number of lines of symmetry.

Question 67:

Match the following:

Solution:

(i) In isosceles triangle number of line of symmetry is 1.
(ii) Number of lines of symmetry in square is 4.
(iii) Number of lines of symmetry in kite is 1.
(iv) Number of lines of symmetry in equilateral triangle is 3.
(v) Number of lines of symmetry in rectangle is 2.
(vi) Number of lines of symmetry in Regular hexagon is 6.
(vii) Number of lines of symmetry in scalene triangle is zero.

Question 68:

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

Solution:

Question 69:

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?

Solution: Yes, they are equal.

Question 70:

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?

Solution:

(a) Yes, the image of P in line l the point P itself.
(b) Yes, PA = PC both are equal.
(c) Yes, PA + PB = PC + PB
(d) Yes, P is that point on line l from which the sum of the distance of points A and B is minimum.

Question 71:

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

Solution:

Question 72:

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′?

Solution:

Yes, AB = A’B’, BC = B’C’ and CA = C’A’ is equal.

Question 73:

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?

Solution:

Question 74:

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

Solution:

Question 75:

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

Solution:

Question 76:

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

Solution:

Question 77:

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

Solution:

Question 78:

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

Solution:

Question 79:

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

Solution:

Question 80:

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?

Solution:

Only one perpendicular can draw in this figure.

Question 81:

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?

Solution:

We can draw only one perpendicular in this fig.

Question 82:

Draw a circle of radius 6cm 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?

Solution:

MN is perpendicular bisector of the diameter XY and perpendicular bisector contains another diameter of the circle.

Question 83:

Bisect ∠XYZ of Fig. 9.22

Solution:

Question 84:

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

Solution:

EFG = 60°
Each parts measure is 15°
= (60°)/4 = 15°

Question 85:

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

Solution:

AMC = 180°
Each parts measure is 90°
= (180°)/2 = 90°

Question 86:

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?

Solution:

ACD = 90°
Each parts measure is 45°
=(90°)/2 = 45°
= ACB = BCD = 45°

Question 87:

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?

Solution:

DBC = DBA + ABC
= 30° + 45°
= 75°

Question 88:

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

Solution:

MN = 6 cm
And these two equal parts of length is 3cm
MN = ON = 3 cm

Question 89:

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

Solution:

MN = 10cm
And these have four equal parts of length
MN = AB = BC = CN = 2.5cm
10cm/4 = 2.5 cm

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NCERT Exemplar Class 6 Maths Symmetry and Practical Geometry Solution