When a transversal intersects two lines, special pairs of angles are formed. If the lines are parallel, those pairs behave in predictable ways: some pairs are congruent (equal in measure) and others are supplementary (their measures add to 180°). This page is about using that fact in reverse — measuring the angles to test whether the lines really are parallel.
As on the Parallel Lines page, the angles are numbered the same way in every activity: ∠1–∠4 at the top intersection (top-left, top-right, bottom-left, bottom-right) and ∠5–∠8 the same way at the bottom intersection. A transversal is a line that intersects two or more other lines at different points, all in the same plane.
If you measure the angles formed by a transversal and find that any one of these conditions holds, you have proved that the lines are parallel:
| If you find… | Example (using this page’s numbering) | …then |
|---|---|---|
| Corresponding Angles are congruent (equal in measure) | ∠2 = ∠6 | the lines are parallel |
| Alternate Interior Angles are congruent (equal in measure) | ∠4 = ∠5 | |
| Alternate Exterior Angles are congruent (equal in measure) | ∠1 = ∠8 | |
| Consecutive Interior Angles are supplementary (their measures add to 180°) | ∠4 + ∠6 = 180° |
One warning: a linear pair being supplementary (adding to 180°) does not prove anything about parallel lines — that is true at every intersection, parallel or not, because a linear pair lives at a single intersection. The same is true of vertical angles being congruent. A real test must compare angles from both intersections.
What to do: The two lines below start out not parallel. Choose an angle-pair type from the menu — the measures for that pair are shown live and keep updating as you work. Drag the handles on the lower line (one at each end) to rotate it until the pair satisfies the parallel condition from the table above. There is no Check button: the feedback is live. The moment the lines are parallel, the activity tells you — and because the line settles into exactly parallel, the angle measures it shows genuinely match. Press New Challenge for a fresh starting position.
Strategy hint: nudge one end of the lower line a little at a time and watch the two measures — you are trying to make them meet. If you chose Consecutive Interior, you are trying to make them add to 180°.
Work through these six questions, one at a time. Each one asks you to use the tests from this page: decide whether lines are parallel, find a measure that would make them parallel, or find the value of x that makes them parallel. The diagrams carry no parallel marks — in these questions, whether the lines are parallel is the whole point. If your first answer is wrong, you will get a hint and another try; the full explanation appears once you answer correctly, or after a second miss. Your score counts first-try answers.