Angles in Parallel Lines (CIE IGCSE Maths: Extended)

What are parallel lines?

• Parallel lines are lines that are always equidistant (ie the same distance apart)
  • no matter how far the lines are extended in either direction, they will never meet.

What are the rules of angles in parallel lines?

• There are 3 main rules:
• 1. Corresponding angles are equal
  • A line cutting across two parallel lines creates four pairs of equal corresponding angles, as shown in the diagram below:

• •  Note: You may also have heard these referred to as ‘F angles’ – do not use that term in an exam or you will lose marks!
     

• 2. Alternate angles are equal

  • A line cutting across two parallel lines creates two pairs of equal alternate angles, as shown in the diagram below:

  

  • Note: You may also have heard these referred to as ‘Z angles’ – do not use that term on an exam or you will lose marks!

• 3. Allied (co-interior) angles add to 180°

  • A line cutting across two parallel lines creates two pairs of co-interior angles
  • In the diagram below, the two coloured angles on the left add up to 180°, as do the two coloured angles on the right:

  

  • Note: These are referred to as either allied or co-interior angles, either is fine to use in the exam
  • You may also have heard these referred to as ‘C angles’ – do not use that term on an exam or you will lose marks!

How do I use the rules of angles in parallel lines?

• Identify any matching angles and any angles that add up to 180°
• STEP 1:
  Identify where the parallel lines are on the diagram
  • They will be marked with arrows or will be in a 2D shape that contains parallel lines
  • You may need to identify them from other reasons, such as vectors
• STEP 2:
  Identify the transverse
  • This is the straight line that extends across both parallel lines
• STEP 3
  Use the information given in the question and the rules above to identify any one of the angles created at the intersection of the transverse and the parallel lines
  • For each transverse crossing one pair of parallel lines there will be four pairs of equal angles
  • Each pair will add up to 180°
• STEP 4
  Fill in all the angles until you find the one you need
  
  • Once you have found the first angle, x°, the others will either also be x° or they will be 180° - x°