Symmetry Powerpoint for revision, more information, school presentation etc...

1. SYMMETRY

2.  A line of symmetry divides a two-dimensional (flat) into two
congruent (identical) shapes.
 Example :
SYMMETRY AND THREE-
DIMENSIONAL SHAPES

3.  A plan of symmetry divides a three-dimensional (solid ) shape
into two congruent solid shapes.
 A cuboid has at least three plans of symmetry , two of which
are shown above.

4.  A shape has reflective symmetry if it has one or more lines or
plans of symmetry.
 A two-dimensional shape has rotational symmetry if, when
rotated about a central point, it fits outline. The number of
times it fits its outline. The number of times it fits its outline
during a complete revolution is called the order of rotational
symmetry.
 Example:

5.  A three-dimensional shape has rotational symmetry if, when
rotated about a central axis, it looks the same at certain
intervals.
 Example:
This cuboid has rotational symmetry of order 2 about the axis shown.

6.  Equal chords and perpendicular bisectors
If chords AB and XY are of equal length, then, since OA, OB, OX
and OY are radii, the triangles OAB and OXY are congruent
isosceles triangles. It follows that:
•The section of a line of symmetry OM through OAB is the
same length as the section of a line of symmetry ON through
OXY.
•OM and ON are perpendicular bisectors of AB and XY
respectively.
CIRCLE PROPERTIES

7.  Tangents from an external point
Triangles OAC and OBC are congruent since <OAC
and <OBC are right angles, OA = OB because they are
both radii, and OC is common to both triangles.
Hence AC = BC.
In general, therefore, tangents being drawn to the
same circle from an external point are equal in
length.

8. THE
END!