Corresponding, alternate and interior angles Corresponding angles are equal a b a = b Alternate angles are equal a b a = b Interior angles add up to 180° a b a + b = 180° Tell pupils that these are called corresponding angles because they are in the same position on different parallel lines. Look for an F-shape Look for a Z-shape Look for a C- or U-shape

Naming triangles Three equal sides and three equal angles. Equilateral triangle Isosceles triangle Two equal sides and two equal angles. No equal sides and no equal angles. Scalene triangle Review the names of these three types of triangle. State that an equilateral triangle is a special name for a regular triangle. Any regular polygon has equal sides and equal angles. Ask pupils to tell you the size of the angles in an equilateral triangle. Ask pupils to give the symmetry properties of each shape.

Naming triangles Triangles can also be named according to their angles. Contains a right angle. Right-angled triangle Acute-angled triangle Contains three acute angles Contains an obtuse angle. Obtuse-angled triangle Ask pupils to explain why it is impossible for a triangle to contain more than one obtuse angle or to contain a reflex angle.

Parallelogram In a parallelogram, opposite sides are equal and parallel. Draw pupils’ attention to the convention of using double dashes to distinguish between the two pairs of equal sides and the use of double arrow heads to distinguish between two pairs of parallel sides. State that when two lines bisect each other, they cut each other into two equal parts. Ask pupils for other derived properties such as the fact that the opposite angles are equal and adjacent angles add up to 180º. Stress, however that a parallelogram has no lines of symmetry. Ask pupils if they know the name of a parallelogram that has four right angles (a rectangle), a parallelogram that has four right angles and four equal sides (a square) and a parallelogram with four equal sides (a rhombus). We can think of a parallelogram as a slanted rectangle. The diagonals of a parallelogram bisect each other. A parallelogram has rotational symmetry of order 2. Opposite angles are equal.

Rhombus A rhombus is a parallelogram with four equal sides. Ask pupils for other derived properties such as the fact that the opposite angles are equal. Ask pupils if they know the name of a rhombus that has four right angles (a square). We can think of a rhombus as a slanted square. The diagonals of a rhombus bisect each other at right angles. A rhombus has two lines of symmetry and it has rotational symmetry of order 2. Opposite angles are equal.

Rectangle A rectangle has opposite sides of equal length and four right angles. Ask pupils for other derived properties such as the fact that the diagonals are of equal length and bisect each other. Ask pupils to explain why it is possible to describe a rectangle as a special type of parallelogram. A rectangle has two lines of symmetry and rotational symmetry of order 2.

Square A square has four equal sides and four right angles. Ask pupils for other derived properties such as the fact that the diagonals are of equal length and bisect each other at right angles. Ask pupils to explain why it is possible to describe a square as a special type of parallelogram, a special type of rhombus or a special type of rectangle. and rotational symmetry of order 4. It has four lines of symmetry

Trapezium A trapezium has one pair of opposite sides that are parallel. It has no lines of symmetry. 2 bottom angles are equal and 2 top angles are equal. Using allied angles the two angles on the left add up to 180, as do the two angles on the right hand side. A trapezium has one line of symmetry when the pair of non-parallel opposite sides are of equal length. It can never have rotational symmetry.

Isosceles trapezium In an isosceles trapezium the two opposite non-parallel sides are the same length. Ask pupils for other derived properties such as the fact that there are two pairs of equal adjacent angles. The diagonals of an isosceles trapezium are the same length. It has one line of symmetry. 2 bottom angles are equal and 2 top angles are equal.

Kite A kite has two pairs of adjacent sides of equal length. Ask pupils for other derived properties such as the fact that there is one pair of opposite angles that are equal. Ask pupils if a kite can ever have parallel sides. Conclude that this could only happen if the four sides were of equal length, in which case it would no longer be a kite, but a rhombus. The diagonals of a kite cross at right angles. A kite has one line of symmetry. One pair of equal angles

Interior angles in regular polygons A regular polygon has equal sides and equal angles. We can work out the size of the interior angles in a regular polygon as follows: Name of regular polygon Sum of the interior angles (no of sides – 2) x180 Size of each interior angle 360 ÷ no of sides Equilateral triangle Square Regular pentagon Regular hexagon 180° 180° ÷ 3 = 60° 2 × 180° = 360° 360° ÷ 4 = 90° 3 × 180° = 540° 540° ÷ 5 = 108° 4 × 180° = 720° 720° ÷ 6 = 120° Ask pupils to complete the table for regular polygons with up to 10 sides.

Lengths in similar shapes In general, if an object is enlarged by a scale factor of k: length = 1 length = k its area or surface area is enlarged by a scale factor of k2 area = 1 area = k2 Generalize the results demonstrated on the previous slide. and its volume is enlarged by a scale factor of k3. volume = 1 volume = k3