1. Welcome
GCSE Maths

3. These shapes have been drawn on a grid of centimetre squares.
Write down the letters of a pair of shapes that are congruent.
Write down the letters of a different pair of shapes that are similar.
Find the perimeter of shape D.

4. Rotational Symmetry
The order of rotational symmetry of a shape is determined by how many times the shape fits onto itself during a 360° turn.

5. A square
order 4
It fits on itself 4 times
We say that a square has…

6. order 1 We say that a heart has…
Every shape has an order of rotational symmetry, even if it is order 1.
order 1
A heart shape fits on itself only once
We say that a heart has…

7. What is the order of rotational symmetry?

8. What is the order of rotational symmetry?

9. What is the order of rotational symmetry?

10. What is the order of rotational symmetry?

12. What will you learn today
What will you learn today? (something you did not know yesterday) By the end of this session I will be able to…
Learners will be able to...
Calculate the interior angles of polygons.
Identify common polygons
Calculate the sum of the exterior angles of any polygon is 360°.
Use the fact that the sum of the interior angle and exterior angle is 180°.
Understand tessellations of regular and irregular polygons.
Explain why some shapes tessellate and why other shapes do not.

13. Polygon comes from latin. Poly- means "many" and -gon means "angle".
What is a polygon?
A polygon is a 2D shape that is made up of straight lines.
They are flat, have 3 or more sides and are closed.
There are two types of polygon, regular and irregular.
Polygon comes from latin. Poly- means "many" and -gon means "angle".

14. These are interior angles – they are on the inside
What do the angles inside a triangle always add up to?
These are interior angles – they are on the inside
180o

15. What do the interior angles of a quadrilateral always add up to?
180o + 180o = 360o

16. Pentagon
180o
180o
180o
3 x 180o = 540o

17. The Formula Sum of interior angles of a polygon = (n-2) × 180
n is the number of sides on the polygon
Find the sum of the interior angles on a dodecagon.
A dodecagon = 12 sides
Formula = (n - 2) × 180
Formula = (12 - 2) × 180
= 1800° 17

18. Find the sum of interior angles for…
Hexagon
Heptagon
Octagon
Nonagon
Decagon

19. Lesson 2

20. Angle facts about regular polygons
Exterior angle =
360° ÷ number of angles

21. Exterior angles This means that the exterior angles
All the exterior angles can fit around a point, as follows:
This means that the exterior angles
on a polygon add up to 360°
Because angles around a point add up to 360 degrees 21

22. Square
The four angles create 360°
360 ÷ 4 = 90°
Exterior angle is 90°

23. Regular Pentagon The five angles create 360° 360 ÷ 5 = 72°
Exterior angle is 72°

24. Regular Hexagon The six angles create 360° 360 ÷ 6 = 60°
Exterior angle is 60°

25. Exterior + Interior = 180° (angles on a straight line =180°)
Adding the exterior and interior angles together always gives a total of 180°
This is true for regular and irregular polygons

26. Find the missing angle 80° 66° 75° 100° 98° 91° A B 95° C 90° 85° 57°
25°
33°

28. Individual study
Applying your knowledge and skills Choose which areas to develop depending on your own strengths and areas
Computers available

29. Reflection of the lesson
What did you learn new today?
Why did you learn it?
How are you going to remember it?