RS Aggarwal 2019,2020 solution class 7 chapter 18 Reflection and Rotational Symmetry Exercise 18B

Exercise 18B

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Question 1:

(i) How many lines of symmetry does an equilateral triangle have?
(ii) What is the order of rotational symmetry of an equilateral triangle?

Answer 1:

(i) An equilateral triangle has 3 lines of symmetry.


(ii) The number of positions a figure can be rotated to, without bringing in any changes to the way it looked originally, is called its order of rotational symmetry.
So, the order of rotational symmetry of an equilateral triangle is 3.
 

Question 2:

Through what different angles should a rectangle be rotated to be in symmetrical position with the original position?

Answer 2:

If we rotate a rectangle by either 180° or 360°, it will look the same as it looked originally, i.e. it will be symmetrical.

Question 3:

What is the order of rotational symmetry of a square? Give the angles of such rotations.

Answer 3:

If we rotate the square either by 90^o, 180^o, 270^o or by 360^o, the square looks exactly the same.
Therefore, the order of rotational symmetry of a square is 4.

Question 4:

(i) How many lines of symmetry does a rhombus have?
(ii) What is the order of rotational symmetry of a rhombus?

Answer 4:

(i) A rhombus has 2 lines of symmetry.

(ii) When we rotate the rhombus either by 180° or by 360°, it looks the same.
Therefore, the rotational symmetry of a rhombus is 2.

Question 5:

Write three letters of the English alphabet which have two lines of symmetry and rotational symmetry of order 2.

Answer 5:

H, O and X are the three letters that have 2 lines of symmetry and their order of rotational symmetry is 2.

Question 6:

Give an example of a figure that has a line of symmetry but does not have rotational symmetry.

Answer 6:

The line of symmetry of an isosceles triangle is the angle bisector of its vertical angle, which is in-between the equal sides. However, it does not have any rotational symmetry.

Question 7:

Does every trapezium have a line of symmetry?

Answer 7:

No, every trapezium does not have a line of symmetry.
Only an isosceles trapezium has a line of symmetry.

Question 8:

What is the line of symmetry of a semicircle?
Does it have rotational symmetry?

Answer 8:

The perpendicular bisector of the diameter of a circle is its line of symmetry.
No, a semicircle does not have any rotational symmetry as it fits itself only once during a complete rotation.

Question 9:

Give an example of a geometrical figure which has neither a line of symmetry nor a rotational symmetry.

Answer 9:

A scalene triangle neither has a line of symmetry nor a rotational symmetry.

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Question 10:

Find
(i) the number of lines of symmetry and
(ii) the order of rotational symmetry of the adjoining figure.
Draw the line of symmetry.

Answer 10:

(i) The line of symmetry of the given figure is 1.
(ii) The order of rotational symmetry of the given figure is 0.

Question 11:

(i) How many lines of symmetry does the given figure have? Draw these lines.
(ii) What is the order of rotational symmetry of the given figure?

Answer 11:

(i) The given figure has 2 lines of symmetry.

(ii) The order of rotational symmetry of the given figure is 2.

Question 12:

Give an example of a letter of the English alphabet which has (i) no line of symmetry and (ii) rotational symmetry of order 2.

Answer 12:

The example of a letter of the English alphabetic system which has (i) no line of symmetry and (ii) rotational symmetry of order 2 is N.