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## Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 4 Geometry Ex 4.2

Miscellaneous Practice problems

Question 1.

Draw and answer the following.

i) A triangle which has no line of symmetry

ii) A triangle which has only one line of symmetry

iii) A triangle which has three lines of symmetry

Solution:

(i) A Scalene triangle has no line of symmetry

(ii) An isosceles triangle has only one

(iii) An equilateral triangle has three lines of symmetry.

Question 2.

Find the alphabets in the box which have

i) No Line of symmetry

ii) Rotational symmetry

iii) Reflection symmetry

iv) Reflection and rotational symmetry

Solution:

i) The alphabets which have no line of symmetry are P, N, S, Z

ii) The alphabets which have Rotational symmetry are I, O, N, X, S, H, Z

iii) The alphabets which have reflection symmetry are A, M, E, D, I, K, O, X, H, U, V, W.

iv) The alphabets which has reflection and rotational symmetry are I, O, X, H.

Question 3.

For the following pictures, find the number of lines of symmetry and also find the order of rotation.

Solution:

The number of lines of symmetry is 0; the order of rotation is 2

ii)

The number of lines of symmetry is 1.

The order of rotation is 0 because it is an isosceles triangle

iii) Number of lines of symmetry are 2

The order of rotation is 2

iv) Number of lines of symmetry 8 and order of rotation 8

v)

The number of the line of symmetry is 1 and the order of rotation 0

Question 4.

The three-digit number 101 has rotational and reflection symmetry. Give five more examples of three-digit number which have both rotational and reflection symmetry.

Solution:

The digits 0, 1, 8 have rotational and reflection symmetry.

∴ The three digits numbers 181, 111, 808, 818, 888 have both rotational and reflection symmetry.

Question 5.

Translate the given pattern and com ilete the design in rectangular strip?

Solution:

Challenge Problems

Question 6.

Shade one square so that it possesses

i) One line of symmetry

ii) Rotational symmetry of order 2

Solution:

Question 7.

Join six identical squares so that atleast one side of a square fits exactly with any other side of the square and have reflection symmetry (any three ways).

Solution:

The required combination of squares are given below.

Question 8.

Draw the following:

Solution:

i) A figure which has reflection symmetry but no rotational symmetry.

ii) A figure which has rotational symmetry but no reflection symmetry.

iii) A figure which has both reflection and rotational symmetry.

Question 9.

Find the line of symmetry and the order of rotational symmetry of the given regular polygons and complete the following table and answer the questions given below.

i) A regular polygon of 10 sides will have ____ lines of symmetry.

ii) If a regular polygon has 10 lines of symmetry, then its order of rotational symmetry is _____

iii) A regular polygon of ‘n’ sides ______ has lines of symmetry and the order of rational symmetry is _____.

Question 10.

Color the boxes in such a way that they possess translation symmetry.

Solution:

The following figures coloured to possess translation symmetry.