This applet shows three important rules about angles, straight lines and triangles

UK - Years 7-9, KS3, Foundation GCSE Mathematics - Shape and Space
US - Grades 9-10, Algebra and Geometry (Graphs)

Instructions below    A smaller version of this applet   See also: Angles and crossed lines  Angles and parallel lines

[Angles, straight lines and triangles]

You can move the points A, B and C by clicking the red dots and dragging them with your mouse.
By moving the points you can investigate three important rules (theorems) about angles. You can choose which rule to investigate from the drop-down list at the bottom of the page.
The sizes of the angles follow these important rules.

What are the rules? Look at the angles marked with blue and orange as you move the lines, and try to work out the rules. They are quite simple.
When you think you know, press the 'Show the Rule' button at the bottom of the screen and the rules will be revealed. Have a think about why these rules work. Enjoy yourself while you practise and learn these rules by name.