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Mathematics · Geometry

Lines, rays and line segments

What is the difference between a line, a ray and a segment — and why do railway tracks never meet?

Points, lines, rays and line segments, intersecting, parallel and perpendicular lines, and where we see them in the world.

5 depths≈ 205 min of reading80 practice questions

The ladder

Choose how deep to go

Every depth is open. Start where it feels interesting — you can always move back.

  1. Discoverabout 25 minStraight paths: points, lines, rays and segmentsMeet points, line segments, rays and lines through everyday things, then see how two lines can cross, meet at square corners or run side by side forever.Owner-accepted · not line-by-line reviewed
  2. Understandabout 40 minNames, notation and rules for linesPin down point, line and plane; name lines, rays and segments correctly; measure without parallax error; and define collinear, concurrent, parallel and perpendicular lines precisely.Owner-accepted · not line-by-line reviewed
  3. Investigateabout 40 minTest it: predictions about points and linesPredict and count how many lines, segments, rays and crossing points some points and lines can make; run a measuring experiment; beat optical illusions; and sort claims into always, sometimes and never true.Owner-accepted · not line-by-line reviewed
  4. Go deeperabout 50 minWhy it must be so: reasoning about linesBuild geometry from Euclid's postulates, prove key facts about intersecting, parallel and perpendicular lines, count with pairs, and follow the 2,000-year story of the parallel postulate from Alexandria to curved space.Owner-accepted · not line-by-line reviewed
  5. Extendabout 50 minLines in the wider worldSee parallel lines meet in perspective drawings, find skew lines in rooms and solids, read lines on maps and sports grounds, meet people who use lines at work, and tackle puzzles from pizza cuts to string art.Owner-accepted · not line-by-line reviewed

Practise and apply

Question bank · 80 questions

9 sections from Foundation to Challenge, each with hints and a worked solution — or play a 10-question round for points and stars.

Foundation 17Core 29Stretch 22Challenge 12

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The web

Connected ideas

Follow a connection when you’re curious — some lead into completely different areas.

Lines, rays and line segments

  • Related to

    Shape and space

    Every polygon is built from line segments, and its sides can be parallel or perpendicular.

  • Helps you understand

    Angles

    An angle is two rays that share an end point; intersecting lines make angle pairs.

Words to know

56 words are explained in these lessons

All vocabulary →

PointLine segmentEnd pointRayLineCurvePlaneIntersecting linesPoint of intersectionParallel linesPerpendicular linesRight angle+44 more