1. Congruence, symmetry and polygons
Congruence and similarity
Symmetry
Properties of quadrilaterals
Names of polygons
Angles in polygons
Properties of regular polygons

2. Congruence and Similarity
Congruent is the maths word that means exactly the same
All 4 of these arrows are congruent. They are the same size and shape
(it doesn’t matter what direction they point in!)

3. Congruence and Similarity
Similar means the shapes are in the same proportion,
but could be a different size
3 of these arrows are similar, but are different sizes.
One is not the same shape... Can you tell which one?

4. Symmetry
A shape has a line of symmetry if the shape looks identical on each
side of the line...
This cross has 4 lines of symmetry.

5. Symmetry A shape has rotational symmetry if it can be turned and still
look identical...
This cross rotational symmetry of order 4.
Have a go at the worksheets on congruence and symmetry....

6. Properties of quadrilaterals
You need to
know and be
able to
recognise
these
Now try the
worksheet...

7. Polygons Polygons are many sided shapes – they can be or regular
irregular
Regular polygon worksheet

8. Angles in a polygon
Do you remember the sum of the angles inside a triangle?
180°
How do we work out the sum of the angles inside other polygons?
We cut them up into triangles ....
Each triangle adds to 180° and so 2 triangles must add to 360°.
This means the INTERIOR angles of a quadrilateral add to 360°...
Look at some more...
This means that the sum of the interior angles for an n sided polygon is
(n-2) x 180°

9. Angles in a polygon So far we have looked at INTERIOR angles
These angles are called EXTERIOR angles.
As you can see, they take you round in a circle.
So the sum of the EXTERIOR angles of a polygon is 360°.

10. Angles in a polygon
So if the shape is a REGULAR polygon, all the exterior angles
are the same...
So, for a pentagon, there are 5 identical exterior angles...
And each one must be 360° ÷ 5 = 72°

11. Angles in a polygon And if the exterior angle is 72°,
The INTERIOR one must be
180° - 72° = 108°
(angles on a straight line)

12. Angles in a polygon Rules to remember:
The sum of the exterior angles is 360° for any polygon.
For regular polygons the exterior angle is
360° ÷ number of sides.
For regular polygons the angle at the centre is also
The interior angle + exterior angle = 180°.
The sum of the interior angles is (n-2)x180° is for a
polygon with n sides.

13. Angles in a polygon Try these:
What is the sum of the interior angles of a polygon with 15 sides?
What is the sum of the interior angles of a polygon with 20 sides?
A regular polygon has 12 sides. What sizes are the interior and
exterior angles?
A regular polygon has 100 sides. What sizes are the interior and
A regular polygon has an exterior angle of 24°. How many sides
does it have?
A regular polygon has an interior angle of 162°. How many sides
Three of the four exterior angles of a quadrilateral are 94°, 50° and 85°.
What’s the fourth exterior angle? How big are the interior angles?