Rotational and Reflectional Symmetry

Rotational and Reflectional Symmetry Oct. 2, 2018

Order 4 Order 2 Order 1 Order 3 Rotational Symmetry All 2 dimensional shapes have some rotational symmetry. The degree of rotational symmetry that an object has is known as its order. For shapes that have “order 2” rotational symmetry or higher, a single centre of rotation can be located. For shapes that have only “order 1” rotational symmetry a centre of rotation can be found anywhere within it. The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees.

Rotational Symmetry The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. Order 1

Rotational Symmetry The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. 2 1 Order 2 Order 1

Rotational Symmetry The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. 2 1 Order 2 Order 1 3 2 1 Order 3

Rotational Symmetry The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. 2 1 Order 2 Order 1 3 3 4 2 1 1 2 Order 4 Order 3

Rotational Symmetry What is the order of rotational symmetry of the shape below?

Rotational Symmetry What is the order of rotational symmetry of the shape below? 5 4 1 2 3 Order 5

Rotational Symmetry What is the order of rotational symmetry of the shape below?

Rotational Symmetry What is the order of rotational symmetry of the shape below? 6 5 1 2 4 3 Order 6

Regular Polygons Equilateral Triangle An equilateral triangle has rotational symmetry of order ?

Equilateral Triangle An equilateral triangle has rotational symmetry of order ?

Equilateral Triangle 3 An equilateral triangle has rotational symmetry of order ? 3 2 1

Square Square A square has rotational symmetry of order ?

Square A square has rotational symmetry of order ?

Square 4 A square has rotational symmetry of order ? 3 4 2 1

Pentagon Regular Pentagon A regular pentagon has rotational symmetry of order ?

Regular Pentagon A regular pentagon has rotational symmetry of order ?

Regular Pentagon 5 A regular pentagon has rotational symmetry of order ? 5 4 1 2 3

Hexagon Regular Hexagon A regular hexagon has rotational symmetry of order ?

Regular Hexagon A regular hexagon has rotational symmetry of order ?

Regular Hexagon 6 A regular hexagon has rotational symmetry of order ? 5 6 1 4 2 3

Octagon Regular Octagon A regular octagon has rotational symmetry of order ?

Regular Octagon 8 A regular octagon has rotational symmetry of order ? 7 8 6 1 5 2 3 4

Rectangle Rectangle A rectangle has rotational symmetry of order ?

Rectangle 2 A rectangle has rotational symmetry of order ? 2 1

Parallelogram A parallelogram has rotational symmetry of order ? Parallelogram

Parallelogram 2 A parallelogram has rotational symmetry of order ? 2 1

Isosceles Triangle An isosceles triangle has rotational symmetry of order ? Isos Tri

Isosceles Triangle 1 An isosceles triangle has rotational symmetry of order ? 1 Isos Tri

Scalene Triangle An scalene triangle has rotational symmetry of order ? Scalene Tri

Scalene Triangle 1 An scalene triangle has rotational symmetry of order ? 1

Isosceles Trapezium An isosceles trapezium has rotational symmetry of order ? Isos Trapezium

Isosceles Trapezium 1 An isosceles trapezium has rotational symmetry of order ? 1

Trapezium A trapezium has rotational symmetry of order ? Trapezium

Trapezium 1 A trapezium has rotational symmetry of order ? 1

Kite A kite has rotational symmetry of order ? Kite

Kite 1 A kite has rotational symmetry of order ? 1

Rhombus A rhombus has rotational symmetry of order ? Rhombus

Rhombus 2 A rhombus has rotational symmetry of order ? 2 1

Ellipse An ellipse has rotational symmetry of order ? Ellipse

Ellipse 2 An ellipse has rotational symmetry of order ? Ellipse 2 1

Rotational Symmetry State the order of rotational symmetry for each shape below: 1 2 3 4 Questions 1 Order 2 Order 3 Order 6 Order 2 7 5 8 6 Order 5 Order 2 Order 3 Order 1 10 9 11 12 Order 4 Order 1 Order 6 Order 8

Rotational Symmetry State the order of rotational symmetry for each shape below: 1 2 3 4 Worksheet 1 7 5 8 6 9 10 11 12

Rotational Symmetry State the order of rotational symmetry for each shape below: 13 14 15 16 Questions 2 Order 5 Order 2 Order 4 Order 1 19 17 20 18 Order 3 Order 6 Order 4 Order 2 22 21 23 24 Order 5 Order 4 Order 3 Order 1

Rotational Symmetry State the order of rotational symmetry for each shape below: 13 14 15 16 Worksheet 2 19 17 20 18 21 22 23 24

REFLECTION Sometimes, a figure has reflectional symmetry. This means that it can be folded along a line of reflection within itself so that the two halves of the figure match exactly, point by point. Basically, if you can fold a shape in half and it matches up exactly, it has reflectional symmetry.

REFLECTIONAL SYMMETRY An easy way to understand reflectional symmetry is to think about folding. Do you remember folding a piece of paper, drawing half of a heart, and then cutting it out? What happens when you unfold the piece of paper?

REFLECTIONAL SYMMETRY Line of Symmetry Reflectional Symmetry means that a shape can be folded along a line of reflection so the two haves of the figure match exactly, point by point. The line of reflection in a figure with reflectional symmetry is called a line of symmetry. The two halves are exactly the same… They are symmetrical. The two halves make a whole heart.

REFLECTIONAL SYMMETRY The line created by the fold is the line of symmetry. How can I fold this shape so that it matches exactly? A shape can have more than one line of symmetry. Where is the line of symmetry for this shape? I CAN THIS WAY NOT THIS WAY Line of Symmetry

Rotational and Reflectional Symmetry