Lines
Segment, ray, line; parallel and perpendicular; real-world examples.
Lines
Lines, Rays, and Segments
What you'll learn
- Distinguish line, ray, line segment.
- Identify parallel and perpendicular lines in the classroom and at home.
- Use correct notation: AB with arrow marks.
Key concepts
Level 1 — Three basic objects
| Object | Symbol | Extends |
|---|---|---|
| Line segment | AB with bar | Both ends fixed — has length |
| Ray | AB with one arrow | One end, goes on forever |
| Line | AB with two arrows | Both directions forever — no end |
Level 2 — Parallel lines
Parallel lines never meet — same distance apart.
Examples: Railway track rails, edges of a door frame (top and bottom), lines on a ruled notebook.
Symbol: AB ∥ CD
Level 3 — Perpendicular lines
Meet at 90° (right angle).
Examples: Corner of a cricket pitch boundary meeting the side line; wall meets floor.
Symbol: AB ⊥ CD
Level 4 — Indian context
On a chess board, rows are parallel to each other; row meets column at right angles.
NCERT anchor: Math-Magic 4, Ch 5 — The Way The World Looks; Ch 11 — Fields and Fences (parallel boundaries)
Worked example
Name parallel and perpendicular lines in a classroom door
Step 1 — Top and bottom of frame are **parallel**.
Step 2 — Left and right sides are **parallel** to each other.
Step 3 — Side meets top at **90°** → **perpendicular**.
Step 4 — Top ⊥ left side ✓
Segment vs ray: draw from A to B and beyond
Step 1 — Segment AB: stop at B.
Step 2 — Ray AB: start at A, pass through B, continue forever.
Step 3 — Ray BA starts at B — **opposite direction** from ray AB.
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| Parallel lines must look equal length on paper | Drawing finite segments | Parallel is about direction, not drawn length |
| Perpendicular means any intersection | Any crossing angle | Must meet at exactly 90° |
| Ray AB and ray BA are the same | Ignoring arrow direction | Rays have starting point — direction matters |
| Lines have a definite length | Confusing line with segment | A segment has length; a line does not |
Quick check
- Railway tracks — parallel or perpendicular?
- What angle do perpendicular lines make?
- Does a ray have one endpoint or two?
- Stretch: How many pairs of parallel lines can you find on a standard Indian postage stamp rectangle? (2 pairs: opposite sides)
Revision tip: Walk around your room and label one parallel pair and one perpendicular pair — geometry is everywhere.
Open the Practice tab for graded questions on Lines, Rays, and Segments.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
Master this topic with Drishti OS
Get unlimited mock tests, AI-powered mentorship, and complete video courses when you join.
Start Free Practice