At the right you can see two parallel lines. You know they are parallel because of the arrow symbols on the lines.

The parallel lines are crossed by another line (in red), which is called a transversal. This line can come from any direction, but if it crosses both of the parallel lines, eight angles are created. The angles are shown in green.

If you know just one of these eight angles, it is possible to calculate all the others.We'll show you how to do this by recognizing patterns.


Supplementary Angles


Here's a pattern you know already.
Angles which form a straight line add up to 180°.



Vertically Opposite Angles (X-Pattern)



Angles across an 'X' are equal.




Alternate Angles (Z-Pattern)



Angles which form a 'Z' pattern are equal.
The 'Z' pattern can be forwards or backwards.

It's the angles inside the corners that are equal.



Corresponding Angles (F-Pattern)



Angles which form an 'F' pattern are equal.
The 'F' pattern can be forwards, backwards, upside down, or upside down and backwards.

It's the angles inside the corners that are equal.




Interior Angles on the Same Side of the Transversal (C-Pattern)

This one is different ... the angles aren't equal!



Angles which form a 'C' pattern are supplementary (add to 180°).
The 'C' pattern can be forwards or backwards.

It's the angles inside the corners of the 'C' that add to 180°.







Now let's practice recognizing the patterns by solving a diagram for all the missing angles.

You only know the top left angle ... it's 100°.

An 'X' pattern gives you another 100° angle.

Then a 'C' pattern gives you 80°.

An 'F' pattern gives you another 100° angle.

A straight line at the top gives you another 80° angle.

Another 'X' pattern gives you another 80° angle.

Finally, a backwards 'Z' pattern gives the final 80° angle.


Here's the final diagram with all the missing angles filled in.

Do you notice other patterns?

One obvious one is that there are only two different angles in the whole diagram.


If you think you're ready, try our parallel lines QUIZ ...


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