Between Lines

Class 7 Maths · Chapter 5: Parallel and Intersecting Lines · NCERT Ganita Prakash section 5.3–5.4

Learn

Railway tracks, the lines of a ruled notebook and the strings of a sitar do not look as if they would ever meet. Lines on the same flat surface (plane) that never meet, however far they are extended, are parallel lines. We write l ∥ m.

l ∥ m

Same plane matters: a line drawn on the table and another on the blackboard may never meet, but they are not called parallel because they lie on different surfaces. Parallel lines stay the same distance apart everywhere.

Paper folding: the opposite edges of a square sheet are parallel and neighbouring edges are perpendicular. Fold it in half: 3 parallel lines (2 edges + 1 crease). Fold again: 5, then 9. Each fold doubles the strips, so n folds give 2ⁿ + 1 lines.

1 fold → 3 · 2 → 5 · 3 → 9

Notation: matching arrow marks (>) on lines show they are parallel; a second set of parallel lines gets double arrows (>>). A small square in the corner marks a right angle between perpendicular lines.

Explore: lines around us.

1. Sort each pair of lines.

Remember

• Parallel lines: same plane, never meet, always the same distance apart.
• Arrow marks show parallel lines; a small square marks a right angle.

Quick check

Which pair of lines is parallel?

1. two lines on a page that stay the same distance apart
2. a line on the floor and a line on the ceiling going different ways
3. two lines that meet far away
4. two lines meeting at 90°

Think about it

How many parallel lines after 4 horizontal folds (counting the two edges)?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.