# Which Quadrilateral Will Always Have 4 Fold Reflectional Symmetry

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Exercise 14.1

Question 1:

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

Question 2:

Express the following in exponential form:

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?

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:

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?

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):

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

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(j) A circle

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

(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.

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?

(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:

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:

Exercise 14.3

Question 1:

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

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.

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(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.

(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?

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:

Question 5:

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

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

Line symmetry:

Rotational symmetry:

Question 6:

After rotating by 60
about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

Other angles will be 120
,180
,240
,300
,360.

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For 60
rotation: It will rotate six times.

For 120
rotation: It will rotate three times.

For 180
rotation: It will rotate two times.

For 360
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) 45                  (ii) 17
?

(i) If the angle of rotation is 45, then symmetry of order is possible and would be 8 rotations.

(ii) If the angle of rotational is 17, then symmetry of order is not possible because 360
is not

completely divided by 17.

### Which Quadrilateral Will Always Have 4 Fold Reflectional Symmetry

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