GCSE MATHSSession 16 – Angles and 2D shapes

Types of angle and properties Angles round the circle, acute, right,

obtuse, reflex

Angles at a point = total 360 Complementary angles = total 90 Supplementary angles = total 180 Vertically Opposite angles = equal the

opposite.

Parallel lines Parallel lines are shown with arrows Where another line crosses both

parallels, the set of angles created will be identical

(mark on any you can easily work out, to help find the ones you need)

Corresponding Alternate Allied

Naming convention

Lowercase letter in the angle.

Angle ABC, is the angle created at point B by the lines AB and BC.

The middle letter in an angle name is always the where the angle is

Ex 23.1 - 10 minutes 1,2,3

Triangles Interior angles add to 180 Acute, obtuse and right angle (name after

the type of the largest interior angle)

Scalene = different sides, different angles Isocolese = two equal sides, 2 equal angles Equilateral = 3 equal sides, 3 equal angles

(60)

Exterior angles

Extend one side to create the exterior angle. Interior + exterior = 180(supplementary)

Ex 23.2 Q3 and 4, Extensions 2, 5 and 6

Quadrilaterals 4 sides shape, 4 angles Interior angles add up to 360

Numerals used to show sides that are the same length

Exercise 23.3 Q 5 Consider the different angle properties, try

different ones until you find something that helps.

Polygons

Many sided shapes Pentagon – 5 sides Hexagon – 6 sides Heptagon – 7 sides Octagon – 8 sides

Remember, interior + exterior angles add up to 180

The exterior angles of a polygon will add up to 360

To work out the total interior angles, split the shape into triangles. Each has 180, so it’s the number of triangles x 180

Ex 23.4

Regular Polygons Regular polygons have equal length sides

and all the angles are equal.

The size of all exterior angles added together is 360, so one exterior angle is 360 divided by the number of sides. Divide 360 by the exterior angle to find the number of sides

Tessellation, regular tessellation

Ex 23.5 Q 1, 4 and 5

Symmetry

Lines of symmetry

Order of rotational symmetry

Tessellation

All the angle at a point have to add up to 360.

If the do not then the shapes will not tessellate.

You may need to work out the interior angles of the given shapes and see if the add up to 360 at the points where they join.

Homework

Create revision notes (p 240) Use BKSB to revise Complete the

homework exam question.