Definition: A transversal is a line that crosses two or more other lines, and when those lines are parallel it creates pairs of equal and supplementary angles.
What is a transversal?
A transversal cuts across other lines. When it crosses two parallel lines, eight angles form.
Which pairs are equal?
- Corresponding angles, in the same position at each crossing
- Alternate interior angles, on opposite sides inside the parallel lines
- Alternate exterior angles, on opposite sides outside
- Vertical angles at each crossing
Which pairs add to 180?
Same-side interior angles are supplementary.
How do you solve a problem?
Alternate interior angles are (3x + 10) degrees and (5x – 20) degrees. Set them equal: 3x + 10 = 5x – 20, so 2x = 30 and x = 15. Each angle measures 55 degrees. The angle next to it on the line measures 180 – 55 = 125 degrees.
Does it work in reverse?
Yes. If corresponding angles are equal, the lines are parallel.
What is a common mistake?
Using these rules when the lines are not parallel. The equal-angle relationships hold only for parallel lines.
Example: If one angle is 72 degrees, its corresponding angle on the parallel line is 72 degrees too.