Regular Shapes, Symmetry, Directions and Maps

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What this lesson covers

  • A regular polygon has all sides the same length and all angles the same size.
  • A line of symmetry splits a shape into two halves that are mirror images.
  • Left and right depend on which way a person is facing.
  • The four compass directions are north, east, south and west.
Key idea

Regular polygons

  • A polygon is a flat shape with straight sides.
  • A regular polygon has all sides equal and all angles equal.
  • A stop sign is a regular octagon. A rectangle that is not a square is not regular.
SidesRegular shape
3equilateral triangle
4square
5regular pentagon
6regular hexagon
7regular heptagon
8regular octagon
9regular nonagon
10regular decagon
Key idea

Try it: regular or not?

Key idea

Lines of symmetry

  • Fold a shape along a line. If the two halves match exactly, the fold is a line of symmetry.
  • One half is the mirror image of the other.
  • To finish a symmetrical picture, copy each part the same distance away on the other side of the line.
  • A regular polygon has as many lines of symmetry as it has sides.
ShapeLines of symmetry
square4
equilateral triangle3
regular hexagon6
rectangle (not a square)2
the letter A1
Key idea

Try it: count the mirror lines

Worked example

Left, right and step-by-step directions

  • Left and right depend on which way you face.
  • If you face a friend, your left hand is on the same side as their right hand.
  • Directions say how far to go and which way to turn.
StepInstruction
1Walk forward 10 m out of the classroom door.
2Make a quarter turn to the left.
3Walk forward 20 m.
4Make a half turn. You now face back the way you came.
Key idea

North, east, south and west

  • A compass shows the four main directions: north, east, south and west.
  • Going clockwise from north: north, east, south, west.
  • On most maps, north is at the top and east is on the right.
  • A quarter turn clockwise from north faces east.
Worked example

Using a map

  • The hall is north of the office.
  • The garden is east of the playground.
  • From the gate, go north 2 squares to reach the field.
a school map, north at the top
WestMiddleEast
NorthFieldHallLibrary
MiddleCar parkOfficeClassrooms
SouthGatePlaygroundGarden

Common mistakes

  • A rectangle is a regular polygon.
    Its sides are not all the same length, so it is not regular.
  • Any line through a shape is a line of symmetry.
    Only a line where both halves match exactly when folded.
  • My left is always your left.
    Left and right depend on which way each person faces.
  • East is on the left of a map.
    On most maps north is at the top, so east is on the right.

Your turn

1

How many sides does a regular hexagon have?

2

How many lines of symmetry does a square have?

3

You face north and make a quarter turn clockwise. Which way do you face now?

4

You face north and make a half turn. Which way do you face now?

5

On the school map, what is east of the hall?

Show answer

1. 6 2. 4 3. East 4. South 5. The library

Summary

What to take away

  • Regular polygons have equal sides and equal angles.
  • A line of symmetry makes two mirror halves.
  • Give directions with turns and distances, or with north, east, south and west.
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