Circles and More Symmetry

Slideshow 38, MathematicsMr Richard Sasaki

Room 307

Objectives• Learn and recall the main properties of circles• Understand how to find lines of symmetry

about a pair of intersecting circles• Complete shapes about set lines of symmetry

and rotational symmetry

Note: Please bring a compass next lesson!

The Circle

CentreRadius

Tangent

DiameterChord

SectorRadii (plural of radius)

CentreCentral Angle

Arc Length

Answers

parallel90 tangents

perpendicular

sizes tangents

2

1A regular pentagon

No, it makes no difference.

Lines of SymmetryWhat is a line of symmetry?It is a line that shows reflection between two congruent sides of a shape.

Lines of symmetry always imply congruence on both sides.

Do congruent sides imply that there is a line of symmetry?Not necessarily. An example of this is the rectangle.This is not a line of symmetry.

Lines of SymmetryIf this was a line of symmetry, what shape would it be?A kite!

Try to remember…Lines of symmetry imply lines of congruence but lines of congruence do not imply lines of symmetry.

Let’s complete some shapes about their lines of symmetry!

Answers – Part 1

Answers – Part 2

Rotational SymmetryIf we know a shape’s order of rotational symmetry, we can draw it in its entirety!ExampleComplete the diagram so that the shape shown has rotational symmetry of order.

Order of Rotation 12

Answers

Order of Rotation 2

Answers

Order of Rotation 24

Answers

Order of Rotation 24

Answers

Order of Rotation 248