Welcome GCSE Maths

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.

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.

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

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…

What is the order of rotational symmetry?

What is the order of rotational symmetry?

What is the order of rotational symmetry?

What is the order of rotational symmetry?

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.

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".

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

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

Pentagon 180o 180o 180o 3 x 180o = 540o

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

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

Lesson 2

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

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

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

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

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

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

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

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

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