Symmetry, Reflection and Rotation — Multiple Choice Questions

The number of lines of symmetry which a quadrilateral cannot have

1. 1

2. 2

3. 3

4. 4

Answer

A kite and an isosceles trapezium are quadrilaterals having 1 line of symmetry.

A rectangle and a rhombus are quadrilaterals having 2 lines of symmetry.

A square is a quadrilateral having 4 lines of symmetry.

There is no quadrilateral having exactly 3 lines of symmetry.

Hence, option 3 is the correct option.

A possible angle of rotation of a figure having rotational symmetry of order greater than or equal to 2 is

1. 36°

2. 144°

3. 150°

4. 360°

Answer

We know that,

If A° is the smallest angle through which a figure can be rotated and still looks the same, then its order of rotational symmetry = $\dfrac{360\degree}{A\degree}$, which must be a whole number greater than or equal to 2.

For 36°, order = $\dfrac{360\degree}{36\degree} = 10$, which is a whole number greater than 2.

For 144°, order = $\dfrac{360\degree}{144\degree} = 2.5$, which is not a whole number.

For 150°, order = $\dfrac{360\degree}{150\degree} = 2.4$, which is not a whole number.

For 360°, order = $\dfrac{360\degree}{360\degree} = 1$, which means the figure has no rotational symmetry.

So, the possible angle of rotation is 36°.

Hence, option 1 is the correct option.

The figure which does not have both line and rotational symmetry is

Answer

The figure in option 1 is a cross. It has 4 lines of symmetry and rotational symmetry of order 4.

The figure in option 2 is a circle with two perpendicular diameters. It has 4 lines of symmetry and rotational symmetry of order 4.

The figure in option 4 is made up of three identical petals. It has 3 lines of symmetry and rotational symmetry of order 3.

The figure in option 3 is made up of three identical bent arms meeting at a point. On rotating it through 120° about this point it looks exactly the same, so it has rotational symmetry of order 3. But there is no line about which it can be folded into two coincident parts, so it has no line of symmetry.

Hence, option 3 is the correct option.

The letter which has both line and rotational symmetry is

Answer

The letter H has two lines of symmetry, one vertical and one horizontal, and it also looks exactly the same on being rotated through 180° about its centre. So, it has rotational symmetry of order 2.

The letter M has one vertical line of symmetry but no rotational symmetry.

The letter S has rotational symmetry of order 2 but no line of symmetry.

The letter Y has one vertical line of symmetry but no rotational symmetry.

So, the letter H has both line and rotational symmetry.

Hence, option 1 is the correct option.