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Chapter 12: Symmetry

    Introduction

    Symmetry

    Lines of Symmetry for Regular Polygons

    Line Symmetry

    Rotational Symmetry

    Line Symmetry and Rotational Symmetry

    Exercise 12.1

    Exercise 12.2

    Exercise 12.3

    What Have We Discussed?

    Extra Curriculum Support

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Chapter 12: Symmetry > Exercise 12.3

Exercise 12.3

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

and are two figures that have both line symmetry and rotational symmetry.

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 rotational symmetry more than one but not a line symmetry:

Hence, it is not possible to draw.

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

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

, if a figure has two or more lines of symmetry, it has rotational symmetry of order more than 1, because every line through the centre forms a line of symmetry and it has rotational symmetry around the centre for every angle.

Fill in the blanks:

ShapeCentre of RotationOrder of RotationAngle of Rotation
Squareintersecting points of °
Rectangleintersecting points of °
Rhombusintersecting points of °
Equilateral Triangleintersecting points of °
Regular Hexagonintersecting points of °
CircleMid-point of
Semi-CircleMid-point of °

Name the quadrilaterals which have both line and rotational symmetry of order more than 1.

, and are the quadrilaterals which have both line and rotational symmetry of order more than 1.

A square has lines of symmetry and rotational symmetry of order .

A rectangle has lines of symmetry and rotational symmetry of order .

A rhombus has lines of symmetry and rotational symmetry of order .

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 °, °, °, °, ° (Enter in ascending order of angle measures).

Can we have a rotational symmetry of order more than 1 whose angle of rotation is (i) 45°? (ii) 17°?

(i) 45° -

Figure can have rotational symmetry of order more than 1 with an angle of rotation of 45°.

(ii) 17° -

Figure cannot have rotational symmetry of order more than 1 with an angle of rotation of 17°.