Module 4 of 6 · MA4-ANG-C-01
Parallel lines
Apply properties of parallel lines cut by a transversal
01
A transversal cuts across
When one line crosses two others it is called a transversal, and it creates eight angles. When the two lines it crosses are parallel, those eight angles come in just two sizes — and every one of them is either equal to, or supplementary with, every other.
02
Corresponding angles (F shape)
Angles in matching positions at the two intersections are equal. Trace an F on the diagram: the two angles sitting in the crook of the F are corresponding, and they are equal.
03
Alternate angles (Z shape)
Angles on opposite sides of the transversal, both between the parallel lines, are equal. Trace a Z: the angles in the two corners of the Z are alternate, and they are equal.
04
Co-interior angles (C shape)
Angles on the same side of the transversal and between the parallel lines are supplementary — they add to 180°, they are not equal. Trace a C. This is the one people get wrong, because they assume every pair is equal.
The rules to know by heart
- Corresponding anglesequal, when the lines are parallel (F)
- Alternate anglesequal, when the lines are parallel (Z)
- Co-interior anglesadd to 180°, when the lines are parallel (C)
- Vertically opposite anglesequal, always — no parallel lines needed (X)
See it work
Try it — move the transversal and watch the pair
122° and 122° — equal. Move the slider as much as you like: corresponding angles on parallel lines stay equal in every position.
A worked example
AB is parallel to CD. Find the size of angle x, and give the reason.
Worked solution
- x = 31°(co-interior angles on parallel lines are supplementary)
Every line has its reason in brackets. In the test, that bracket is worth marks on its own — write it even when the number feels obvious.
Words for this module
Transversal
A line that crosses two or more other lines.
Corresponding angles
Angles in matching positions at the two intersections — the F shape. Equal when the lines are parallel.
Alternate angles
Angles on opposite sides of the transversal, between the parallel lines — the Z shape. Equal when the lines are parallel.
Co-interior angles
Angles on the same side of the transversal, between the parallel lines — the C shape. They add to 180°.
Watch out: The only parallel-line pair that is NOT equal. If your two angles look different sizes and are both inside on the same side, they're co-interior.
ready?
Practise until you get five in a row.