Symmetry&

Congruence

CongruenceThis is where shapes are identical in size

and only differ in their presentation. (may be rotated)

All angles must be the same!!

All sides must be the same length!!

Look at these shapes:

AB C D

E

Shapes A, C and E are congruent, trace one shape and fit it over the others they have only been rotated!!

Shapes B & E are congruent but differ from (A, C & D)

Using tracing paper is the ideal way of checking for congruence

Line Symmetry• Symmetry is essential to our lives!!• We decide a mate by looking for symmetry in

their facial features at first contact.• Try for yourselves:

– Get a photograph, cut it in half vertically– Scan the two halves separately– Reflect the image using computer graphics and stitch the

reflected image back to it’s original half– Look at the two different pictures produced!!!

The closer the two images appear, the more ‘perfect’ (aesthetically pleasing) your original features are.

Models present a near perfect facial image, the two halves of their face are as near identical as possible!!!!

Line Symmetry

• If a shape can be folded in half so that one half fits exactly on top of the other, then we say that the shape has got line symmetry.

• The fold is called a line of symmetry.• This shape has got a vertical line of symmetry.

Line Symmetry in the Alphabet

Which letters have got lines of symmetry?

A B C D E F G H I

J K L M N O P Q R

S T U V W X Y Z

Click to see the lines of symmetry.

Lines of Symmetry all around usWhich of these road signs have got lines of symmetry?

Click to see the lines of symmetry.

Rotational Symmetry• If, when you rotate a shape, it looks exactly

the same as it did in its original position, then we say that the shape has got rotational symmetry.

• This square has got rotational symmetry.

• It looks exactly the same four times in a full turn.• It has got rotational symmetry order 4.

Rotational Symmetry• Does this rectangle have rotational symmetry?

• It looks exactly the same twice in a full turn.• It has got rotational symmetry order 2.

Rotational Symmetry in the Alphabet

Which letters have got rotational symmetry?

A B C D E F G H I

J K L M N O P Q R

S T U V W X Y Z

Click to see the answers.

Order 2 Order 2 Order 2

Order 2 Order 2 Order 2

Order 2

Rotational Symmetry all around usWhich road signs have got rotational symmetry?

Click to see the answers.

Rotational Symmetry all around usClick to see the road signs with rotational symmetry.

Order 3 Order 2 Order 2

Rotational Symmetry all around usClick to see more road signs with rotational symmetry.

Order 4 Order 3 Order 2

Rotational Symmetry all around usClick to see more road signs with rotational symmetry.

Order 3 Order 2