Two or more lines are parallel when they lie in the same plane and do not intersect — no matter how far they are extended in either direction. Because parallel lines never intersect, they point in exactly the same direction and stay the same distance apart everywhere. Parallelism is not limited to a single pair: three or more lines can all be parallel to one another. On a diagram, matching arrowheads on the lines are the standard way of saying “these lines are parallel.”
The red line and the blue line below are parallel in each picture. Notice that the gap between them never changes, and the small arrowheads match — one arrowhead on each line in the first picture, two on each line in the second. The arrowheads point along the direction of their line. Matching marks always mean “parallel” (or, on other diagrams, “equal”).
What to do: A line is drawn on the grid. Press and drag anywhere in the box to draw your own line, then let go. Your job is to draw a line that is parallel to the one shown — same direction, any starting point, any length (but not right on top of it). Press Next for a new direction to try.
Before we look at parallel lines, start with something smaller. When one line is intersected by another line, exactly four angles are formed at the intersection. Those four angles are numbered ∠1 to ∠4 below, and the measure of each angle is shown.
The intersecting line is called a transversal. A transversal is a line that intersects two or more other lines at different points, all in the same plane. In this activity, the transversal begins by intersecting just one line — then you will slide in a second line for it to intersect.
What to do: Drag the big orange handle down along the transversal (or press Play, or use the slider). A second line slides into view. It stays parallel to the first line the whole time, and it creates a second intersection — with four more angles, ∠5 to ∠8. Watch the measures as it moves: the new angles repeat the pattern of the first four. You can also drag the purple handle at the top to tilt the transversal, and every measure updates live.
What to notice: ∠2 and ∠6 have the same measure, ∠1 and ∠5 match, and so on. That repetition is the whole story of this page — the rest of the activities just name the different matching pairs.
Now put the two parallel lines and the transversal together. Eight angles are formed, and they fall into pairs that have special names and predictable measures. In every activity on this page, the angles are numbered the same way: ∠1–∠4 at the top intersection (top-left, top-right, bottom-left, bottom-right) and ∠5–∠8 the same way at the bottom intersection.
What to do: Choose a name from the list. That pair of angles lights up on the diagram, and the readout underneath tells you the relationship. Most types have more than one pair in the diagram, so the highlighting cycles through them automatically — you can also step through them yourself with the ◀ Previous Pair and Next Pair ▶ buttons. The Parallel button is on by default: turn it off and the bottom line tilts, so you can see which relationships depend on the lines being parallel (and which two — vertical angles and linear pairs — are true whenever lines intersect, parallel or not).
Two reminders from a single intersection — Linear Pair and Vertical Angles: A linear pair is two angles that sit side by side on a straight line. Because a straight line measures 180°, a linear pair is always supplementary: the measures of its two angles add to 180°. Vertical angles are the angles opposite each other where two lines intersect, and they are always congruent: their measures are equal. Notice that both of these pairs live at just one intersection, so neither one depends on parallel lines at all — each is true whenever any two lines intersect. Linear pairs are often the missing step in angle problems: find one angle, and the measure of its linear-pair partner is just 180° minus it.
What to do: Drag any of the round handles to move the lines and the transversal around. Pick an angle type from the menu and that pair lights up and cycles, with live measures — so you can test for yourself whether the relationship survives when you move things. With Parallel on, the bottom line is locked to the same direction as the top line: dragging the top line swings both, and dragging the bottom line slides it without rotating it. Turn Parallel off to move every line completely freely and watch the “parallel-only” relationships break. All Angles shows all eight measures at once, and One at a Time walks through the angles one by one.
Ready to practice? Work through these six questions, one at a time. In every diagram the lines are parallel (look for the matching arrowhead marks), and the angles use this page’s 1–8 numbering. 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.