Lines and Angles
90. The Transversal Bridge · crossing lines, creating angle pairs
The transversal always cuts both lines, forming the same eight angle positions.
A transversal is a line that cuts across two or more other lines. When it crosses two lines, it creates 8 angles (4 at each intersection), grouped into pairs: corresponding, alternate (interior and exterior), and co-interior.
What this lesson covers
Try to break it
Try dragging T slowly. Notice that angles in the same relative position at each intersection stay matched. These matching positions are called corresponding angles. The angles between the lines are interior; outside are exterior.
How you build it
Draw two parallel lines and a transversal crossing both.
- Draw the first straight line, L₁.
- Use the parallel tool: click below the first line, then click on that line.
- Draw the transversal T — a line that cuts across both L₁ and L₂.
- Mark point I1 where the transversal crosses the first line.
- Mark point I2 where the transversal crosses the second line.
The proof, step by step
Prove that a transversal cutting two lines forms eight angles.
- A transversal creates eight angles at two intersection points.
- Interior angles lie between the two lines; exterior angles lie outside.
- Alternate angles are on opposite sides of the transversal.
- Corresponding angles occupy the same relative position at each intersection.
- Allied (co-interior) angles are on the same side of the transversal and between the lines.
Worked example
In the figure, lines L₁ and L₂ are parallel and T is a transversal. If ∠3 = 70°, find the measure of ∠5.
Since L₁ || L₂ and T is a transversal, alternate interior angles are equal. ∠3 and ∠5 are alternate interior angles. Therefore, ∠5 = ∠3 = 70°.
- 70° — correct
- 110°
- 90°
- 180°