Part 4: Geometry and measures

• A point is a dot or cross on a diagram that can be labelled. Points can be connected by either straight or curved lines, and linked together to form shapes

  
• Lines and points form shapes. Shapes can have any number of points and lines.
• 2-Dimensional shapes exist in two dimensions – width and height.

  
• Shapes can have reflectional or rotational symmetries
• Reflectional symmetry is easy to see because one side of a shape is the same (or a reflection of) the other half

  
• A shape with rotational symmetry will still look the same after it has been rotated (turned around a point) by less than one full turn

  
• Types of angle

  A) Acute

  B) Obtuse

  C) Reflex

  
• Interior angles are on the inside of the shape at the vertex

  
  

  Exterior angles are measured outside of the shape from the extension of one side to the next side.

  
• Perpendicular lines meet at a 90 degree angle

  
• A perpendicular bisector is a line that cuts another line exactly halfway through it. It bisects the line at a right angle.

  
• Bisecting an angle involves constructing a line that cuts an angle exactly in half

  
• A locus (loci plural) is a set of points that follows a certain location rule, for example, always being 3 m away from a point.
• The angles around a point add up to 360 degrees
• The angles on a straight line add up to 180 degrees
• Corresponding angles are equal. They are on the same side of the transversal line and the lines on which the angles lie on form an ‘F’ shape.

  
• Alternate angles are equal. They are on opposite sides of the transversal line and the lines on which they lie form a ‘Z’ shape

  
• Vertically opposite angles are also equal.

  
• Equilateral triangle:

  • All sides are equal length
  • All angles are 60 degrees

  
• Isosceles triangle:

  • 2 sides are equal in length
  • 2 angles are equal in size

  
• Scalene triangle:

  • No sides are equal in length
  • No angles are equal in size

  
• Square:

  • 2 pairs of parallel sides
  • 4 equal side lengths
  • 4 equal angles of 90 degrees

  
• Rectangle:

  • 2 pairs of parallel sides
  • 2 pairs of equal side lengths
  • 4 equal angles of 90 degrees

  
• Rhombus:

  • 2 pairs of parallel sides
  • 4 equal side lengths
  • Opposite angles are equal

  
• Trapezium:

  • 1 pair of parallel sides

  
• Isosceles Trapezium:

  • 1 pair of parallel sides
  • 1 pair of opposite sides with equal length
  • 2 pairs of adjacent equal angles

  
• Two shapes are similar if they are the same shape but one may be an enlargement of the other.

  
• Two shapes are congruent if they are exactly the same shape and have the same size.

  
• Translations involves moving the shape in different directions without making any changes to the size of the original shape.
• Centre of rotation: The fixed point around which the shape is turned.
• The centre of the circle is the point that is at an equal distance from all the points on the circumference of the circle

  
• The radius is a line that joins the centre of the circle with a point on the circumference.

  
• The diameter is a line that joins a point on the circumference with another point on the circumference and passes through the centre point.

  
• The circumference is also known as the perimeter of the circle and defines the distance around the outside of the circle

  
• A tangent is a line that touches the circle at only one point. The tangent meets the radius at a perpendicular angle (90°).

  
• An arc is a portion of the circumference of the circle.

  
• A chord is a straight line joining two points on the circumference

  
• A sector of a circle is a portion of a circle and is “pie-shaped”. Its perimeter is made up of two radii and a portion of the circumference (arc).

  
• A segment of a circle is the area enclosed by an arc and a chord of the circle.

  
• Circle theorem 2: Angle at the centre of the circle is twice the angle at the circumference

  
• Circle theorem 1: When a radius meets a tangent, the angle will always be 90 degrees