Corresponding, alternate and interior angles

1. Corresponding, alternate and interior angles Corresponding angles are equal Alternate angles are equal Interior angles add up to 180° a a a b b b a = b a = b a + b = 180° Look for an F-shape Look for a Z-shape Look for a C- or U-shape

2. Naming triangles Isosceles triangle Scalene triangle Equilateral triangle Three equal sides and three equal angles. Two equal sides and two equal angles. No equal sides and no equal angles.

3. Naming triangles Right-angled triangle Acute-angled triangle Obtuse-angled triangle Contains a right angle. Contains three acute angles Contains an obtuse angle. Triangles can also be named according to their angles.

4. Parallelogram In a parallelogram, opposite sides are equal and parallel. The diagonals of a parallelogram bisect each other. A parallelogram has rotational symmetry of order 2. Opposite angles are equal.

5. Rhombus A rhombus is a parallelogram with four equal sides. 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.

6. Rectangle A rectangle has opposite sides of equal length and four right angles. A rectangle has two lines of symmetry and rotational symmetry of order 2.

7. Square A square has four equal sides and four right angles. It has four lines of symmetry and rotational symmetry of order 4.

8. 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.

9. Isosceles trapezium In an isosceles trapezium the two opposite non-parallel sides are the same length. 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.

10. Kite A kite has two pairs of adjacent sides of equal length. The diagonals of a kite cross at right angles. A kite has one line of symmetry. One pair of equal angles

11. Interior angles in regular polygons Equilateral triangle 180° 180° ÷ 3 = 60° Square 2 × 180° = 360° 360° ÷ 4 = 90° Regular pentagon 3 × 180° = 540° 540° ÷ 5 = 108° Regular hexagon 4 × 180° = 720° 720° ÷ 6 = 120° 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:

12. Lengths in similar shapes length = 1 length = k In general, if an object is enlarged by a scale factor of k: area = 1 area = k2 its area or surface area is enlarged by a scale factor of k2 volume = 1 volume = k3 and its volume is enlarged by a scale factor of k3.