Eight angles, two numbers
One line crosses two parallel ones and makes eight angles. There are only two different sizes among them. Pick a pair, turn the crossing line, and see which fact survives.
55° = 55°
Corresponding angles: the same corner at each crossing. Turn the crossing line and both numbers move, equal the whole way.
- The pair
- Corresponding
- The crossing line
- 55°
- The two lines
- Parallel
Drag the orange crossing line to turn it, and the ring on the lower line to tilt it out of parallel.
Which pair?
Ready to try some? Angles in parallel lines worksheets
Where it usually goes wrong
Corresponding and alternate angles get remembered as shapes — the F and the Z — and then used on any two lines a third one crosses. The equal-angle rules need the two lines to be parallel. Take the parallel away and the letters are still there in the diagram and the angles are no longer equal.
Try this
- Pick Corresponding and turn the crossing line. Both numbers move together and stay equal the whole way.
- Now drag the ring to tilt the lower line out of parallel. The pair comes apart, and the F is still sitting there in the picture.
- Switch to Alternate and to Co-interior. One pair is equal, one pair adds to 180°, and only while the lines are parallel.
Where this goes next
Angle chasing — finding one angle to find the next — is how most geometry proofs move, and every step of it depends on knowing which fact you are allowed to use.