Angles with parallel lines
Drag and turn two parallel lines and a transversal to see which angles always stay equal, which add up to 180°, and what happens when the lines are not parallel. Then use a parallel line to show why a triangle's angles add up to 180°.
- UK: Year 8
- France: grade 6
- Germany: grade 7
- Iran: grade 7
- Afghanistan: grade 7
- Syria: grade 6
- Palestine: grade 4
- Ukraine: grade 7
- Russia: grade 7
Guide
For Years 7–8 (KS3: parallel lines, alternate and corresponding angles). The coloured dots can be dragged; the hollow ring turns the transversal. The readouts under the figure show the angles live.
AB is parallel to CD, and the line EF crosses them: EF is a transversal. The angles are labelled with small letters: a to d at E and e to h at F (a at the top left, then clockwise). The figure shows the ones we need: b, d, e and f.
Slide AB down without turning it until it lies on CD: angle b lands exactly on angle f, so they are equal (corresponding angles, the F shape). Angles d and f are equal too (alternate angles, the Z shape). Angles d and e, both between the lines on the same side of the transversal, are co-interior (the C shape): they are not equal, they add up to 180°.
These facts are only true when the lines really are parallel. The converse is true too: if a transversal makes equal alternate (or corresponding) angles, the lines are parallel. The little arrows on the lines appear only while the lines really are parallel.