Reflection and rotation symmetry - Assets

1 101 Reflection and rotation symmetry1 Reflection and rotation symmetry This work will help you recognise Reflection symmetry and rotation symmetry in a shape complete a shape with given Reflection or rotation symmetry name types of triangle and quadrilateral, and recognise symmetrical and regular polygonsYou need sheets F1 1, F1 2, F1 3 and F1 many lines of symmetry has each of these shapes?(a)(b)(c)(d)(e)A2 This question is on sheet F1 question is on sheet F1 each diagram and follow the instruction below it.(a)(b)(c)(d)AReflection symmetry level 4A shape with Reflection symmetryhas oneor more mirror lines that reflect one halfof the shape exactly on to the other mirror lines are called lines of shape has twolines of two moresquares to make apattern with 2lines of two moresquares to make apattern with 1 lineof three moresquares to make apattern with 4lines of two moresquares to make apattern with 1 lineof symmetry .

2 Cambridge University University Press978-0-521-69431-5 - SMP Interact Foundation 1 The School Mathematics ProjectExcerptMore information1 Reflection and rotation symmetry11B1 What is the order of rotation symmetry of each of these?(a)(b)(c)(d)B2 This question is on sheet F1 each diagram and complete it as stated.(a)(b)(c)B4 Copy this diagram and shade two more squaresso that it has rotation symmetry of order symmetry A shape with rotation (or rotational) symmetrycan be rotated round its centre so that it fits on top of itself more than one order of rotation symmetry is the number of different positions a shape fits on top of say that a shape with no rotation symmetryhas order 1as it fits on top of itself in only one shape hasrotation symmetryof order two more squaresso that the final shapehas rotation symmetryof order three more squaresso that the final shapehas rotation symmetryof order three more squares so that the final shape has norotation symmetry .

3 Cambridge University University Press978-0-521-69431-5 - SMP Interact Foundation 1 The School Mathematics ProjectExcerptMore information121 Reflection and rotation symmetryC1 For each design below(i)write down how many lines of symmetry it has(ii)write down the order of rotation symmetry (a)(b)(c)(d)(e)(f )(g)(h)C2 This question is on sheet F1 types of symmetry A shape can have Reflection symmetry and rotation symmetryThis shape has Reflection symmetry but no rotation symmetry . How many lines ofsymmetry does it have?This shape has rotation symmetry but no Reflection symmetry . What is its order ofrotation symmetry ?This shape has bothreflection and rotationsymmetry. Describe the symmetryof this Cambridge University University Press978-0-521-69431-5 - SMP Interact Foundation 1 The School Mathematics ProjectExcerptMore information1 Reflection and rotation symmetry13D1 This diagram shows a regular hexagon split into four many of these triangles are isosceles?

4 D2 Here is another way to split up a regular is the name of the quadrilateral in this hexagon?D3 Show how to split up a regular hexagon into(a)a rectangle and two isosceles triangles(b)two trapeziums(c)three rhombuses(d)an equilateral triangle and three isosceles trianglesD4 Draw an isosceles clearly any lines of (a)Draw a rectangle and show any lines of symmetry it has.(b)What order of rotation symmetry does a rectangle have?D6 Describe the symmetry of a a trapezium that has no Reflection triangles and quadrilaterals A mosaic pattern is made by joining the centres of regular is part of the pattern withsome shapes shaded. What kind of triangle is shape A? Name each of the shadedquadrilaterals. How many lines of symmetryhas each shape? What is the order of rotationsymmetry of each shape?ABCEDT Cambridge University University Press978-0-521-69431-5 - SMP Interact Foundation 1 The School Mathematics ProjectExcerptMore information141 Reflection and rotation symmetryE1 All these shapes are hexagon has(a)only one line of symmetry (b) rotation symmetry butno Reflection symmetry (c) rotation symmetry of order 3 and 3 lines of symmetry (d)no Reflection or rotation symmetryLines that join corners across a shape are called its each quadrilateral by the given information.

5 (a)(b)(c)(d)(e)ESymmetrical and regular polygons A polygonis a shape with straight polygons that have special names are shown in this diagonals of thisquadrilateral are not thesame length and do notcross at right have rotationsymmetry of order diagonals crossat right diagonals are thesame have rotationsymmetry of order have Reflection symmetrybut no rotation diagonals cross at diagonals are thesame have rotationsymmetry of order have no have two pairs ofparallel of sidesName of polygon3triangle4quadrilateral5pentagon6 hexagon8octagon10decagon Cambridge University University Press978-0-521-69431-5 - SMP Interact Foundation 1 The School Mathematics ProjectExcerptMore informationE4 Here are some regular polygons.(a)Copy and complete this table.(b)An icosagon is a polygon with 20 symmetry does a regular icosagon have?E2 Here are some of these polygons is(a)a pentagon with Reflection symmetry (b)an octagon with Reflection symmetry but no rotation symmetry (c)a hexagon with rotation symmetry but no Reflection symmetry (d)an octagon with rotation symmetry but no Reflection symmetryE3 Draw a decagon with only one line of Reflection and rotation symmetry15 PolygonNumber Lines ofOrder of rotationof sidessymmetrysymmetryEquilateral triangle333 Square4 Regular pentagon5 Regular hexagonRegular nonagonpentagonhexagonnonagonABCDEGFA polygon that has all its edges equal and all its angles equal is called a regular polygon.

6 Cambridge University University Press978-0-521-69431-5 - SMP Interact Foundation 1 The School Mathematics ProjectExcerptMore informationF1 Each shape in this diagram is one half of a quadrilateral has line M as a line of the diagram.(a)Draw a Reflection of each shape in line M.(b)Write down the coordinates of each corner ofthe rhombus.(c)Write down the name of the other shape in this diagram is part of a x-axis is a line of symmetry of the hexagon.(a)Copy the diagram and complete the hexagon.(b)Write down the coordinates of each corner ofthe hexagon.(c)How many lines of symmetry does the hexagon have?F3 This diagram shows half a quadrilateral has rotation symmetry of order 2.(a)(i)Copy the diagram and complete the quadrilateral.(ii)What are the coordinates of the fourth corner of the quadrilateral?(b)What is the name of this quadrilateral?(c)How many lines of symmetry does the quadrilateral have?

7 F4 Draw a grid going from 4 to 4 on both axes.(a)Draw a straight line from (2, 0) to (2, 3).Then draw a straight line from (2, 3) to ( 2, 0).(b)(i)Add another point to make a quadrilateral with rotation symmetry of order 2.(ii)What are the coordinates of this point?161 Reflection and rotation symmetry 0 123456776543210 Mxyxy3210 1 2 3 3 2 1 0 123xy3210 1 2 3 3 2 1 0 123 FUsing coordinates Cambridge University University Press978-0-521-69431-5 - SMP Interact Foundation 1 The School Mathematics ProjectExcerptMore information1 Reflection and rotation symmetry17 Test yourselfT1 Here are four road of these road signs have one line of symmetry .(a)Write down the letters of each of these two road one of these four road signs has rotational symmetry .(b)(i)Write down the letter of this road sign.(ii)Write down its order of rotational has lots of tiles, all like this one.(a)Judith makes these each pattern, write down the number of lines of symmetry it the pattern does not have Reflection symmetry , write 0.

8 (i)(ii)(iii)(iv)(v)(b)Copy and complete this tiling pattern so thatit has rotation symmetry of order design is made from a regular hexagon andfour equilateral triangles.(a)What is its order of rotation symmetry ?(b)Write down the number of lines of symmetry it Cambridge University University Press978-0-521-69431-5 - SMP Interact Foundation 1 The School Mathematics ProjectExcerptMore informatio