Class 7 - Maths - Symmetry

Exercise 14.1

Question 1:

Copy the figures with punched holes and find the axes of symmetry for the following: Answer:  Question 2:

Express the following in exponential form: Answer: Question 3:

In the following figures, the mirror line (i.e., the line of symmetry) is given as a dotted line.

Complete each figure performing reflection in the dotted (mirror) line.

(You might perhaps place a mirror along the dotted line and look into the mirror for the image).

Are you able to recall the name of the figure you complete? Answer:  Question 4:

The following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry: Identify multiple lines of symmetry, if any, in each of the following figures: Answer:  Question 5:

Copy the figure given here:

Take any one diagonal as a line of symmetry and shade a few more squares to make the figure symmetric about a diagonal.

Is there more than one way to do that? Will the figure be symmetric about both the diagonals? Answer:

Answer figures are: Yes, there is more than one way.

Yes, this figure will be symmetric about both the diagonals.

Question 6:

Copy the diagram and complete each shape to be symmetric about the mirror line(s): Answer: Question 7:

State the number of lines of symmetry for the following figures:

(a) An equilateral triangle                     (b) An isosceles triangle                   (c) A scalene triangle

(d) A square                                             (e) A rectangle                                    (f) A rhombus

(g) A parallelogram                                (h) A quadrilateral                              (i) A regular hexagon

(j) A circle

Answer:  Question 8:

What letters of the English alphabet have reflectional symmetry (i.e., symmetry related to mirror reflection) about.

(a) a vertical mirror       (b) a horizontal mirror       (c) both horizontal and vertical mirrors

Answer:

(a) Vertical mirror – A, H, I, M, O, T, U, V, W, X and Y (b) Horizontal mirror – B, C, D, E, H, I, O and X (c) Both horizontal and vertical mirror – H, I, O and X.

Question 9:

Give three examples of shapes with no line of symmetry.

Answer:

The three examples are:

1. Quadrilateral 2. Scalene triangle 3. Parallelogram

Question 10:

What other name can you give to the line of symmetry of:

(a) an isosceles triangle?                     (b) a circle?

Answer:

(a) The line of symmetry of an isosceles triangle is median or altitude.

(b) The line of symmetry of a circle is diameter.

Exercise 14.2

Question 1:

Which of the following figures have rotational symmetry of order more than 1: Answer:

Rotational symmetry of order more than 1 are (a), (b), (c), (d), (e) and (f) because in these

figures, a complete turn, more than 1 number of times, an object looks exactly the same.

Question 2:

Give the order the rotational symmetry for each figure: Answer:   Exercise 14.3

Question 1:

Name any two figures that have both line symmetry and rotational symmetry.

Answer:

Two figures that have both line symmetry and rotational symmetry are:

Circle and Square.

Question 2:

Draw, wherever possible, a rough sketch of:

(i) a triangle with both line and rotational symmetries of order more than 1.

(ii) a triangle with only line symmetry and no rotational symmetry of order more than 1.

(iii) a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.

(iv) a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.

Answer:

(i) An equilateral triangle has both line and rotational symmetries of order more than 1.

Line symmetry: Rotational symmetry: (ii) An isosceles triangle has only one line of symmetry and no rotational symmetry of order

more than 1.

Line symmetry: Rotational symmetry: (iii) It is not possible because order of rotational symmetry is more than 1 of a figure, most a certain the line of symmetry.

(iv) A trapezium which has equal non-parallel sides, a quadrilateral with line symmetry but not

a rotational symmetry of order more than 1.

Line symmetry: Rotational symmetry: Question 3:

If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?

Answer:

Yes, because every line through the centre forms a line of symmetry and it has rotational

symmetry around the centre for every angle.

Question 4:

Fill in the blanks: Answer: Question 5:

Name the quadrilateral which has both line and rotational symmetry of order more than 1.

Answer:

Square has both line and rotational symmetry of order more than 1.

Line symmetry: Rotational symmetry: Question 6:

After rotating by 600 about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

Answer 6:

Other angles will be 1200 ,1800 ,2400 ,3000 ,3600.

For 600 rotation: It will rotate six times.  For 1200 rotation: It will rotate three times. For 1800 rotation: It will rotate two times. For 3600 rotation: It will rotate one time. Question 7:

Can we have a rotational symmetry of order more than 1 whose angle of rotation is:

(i) 450                  (ii) 170 ?

Answer:

(i) If the angle of rotation is 450, then symmetry of order is possible and would be 8 rotations.

(ii) If the angle of rotational is 170, then symmetry of order is not possible because 3600 is not

completely divided by 170.

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