Edexcel IGCSE Maths 复习笔记 4.1.1 Angles in Parallel Lines

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.

Working with 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 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 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. 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 sometimes referred to as allied angles, which is fine. You may also have heard these referred to as ‘C angles’ – do not use that term on an exam or you will lose marks!

4. Vertically opposite angles are equal

• Whenever two straight lines cross, they create two pairs of equal vertically opposite angles, as in the diagram below:

• Don’t forget this rule when answering parallel line questions! For example, in the following diagram the highlighted angles are equal:

• Note: vertically opposite angles are sometimes simply called opposite angles. Either term will get you the marks

5. Angles on a line add to 180°

• This rule is also still true with parallel line questions! In the following diagram, for example, the highlighted angles add up to 180°:

Then:6. Just angle chase!