NCERT Solutions for Class 7th Maths Chapter 5 Parallel and Intersecting Lines
Updated on 2026-09-19
About this chapter
When two lines intersect, four angles are formed. Linear pairs add up to 180° and vertically opposite angles are equal. If all four angles at a crossing are equal, each is 90° and the lines are perpendicular . Parallel lines lie in the same plane and never meet, however far they are extended. They are marked with matching arrow heads. A transversal cutting two lines makes 8 angles, with at most 4 different sizes. Corresponding angles are equal exactly when the two lines are parallel — this is the test for parallelism. For a transversal across parallel lines: alternate angles are equal, and interior angles on the same side add up to 180°.
- Across the Line
- Perpendicular Lines
- Between Lines
- Parallel and Perpendicular Lines in Paper Folding
- Paper Folding, and Notations
- Transversals and 5.6 Corresponding Angles
- Corresponding Angles
- Drawing Parallel Lines
- Alternate Angles
- Parallel Illusions
Quick revision
| Idea | What it means | Where it appears | Key result |
|---|---|---|---|
| Intersecting lines | Two lines of a plane that meet at a point | Fig. 5.2 | Four angles are formed |
| Linear pair | Two adjacent angles standing on a straight line | ∠a and ∠b, Fig. 5.2 | Sum = 180° |
| Vertically opposite angles | The two facing angles at a crossing | ∠b and ∠d, Fig. 5.2 | Always equal |
| Perpendicular lines | Lines crossing so that all four angles are equal | Fig. 5.4 | Each angle = 90° |
| Parallel lines | Lines of one plane that never meet | Fig. 5.6 | Marked with >, >> arrow heads |
| Transversal | A line that cuts a pair of lines | t in Fig. 5.14 | 8 angles, at most 4 sizes |
| Corresponding angles | Same position at the two crossings | ∠1 and ∠5, Fig. 5.14 | Equal ⟺ the lines are parallel |
| Alternate angles | Opposite sides of the transversal, one at each line | ∠d and ∠f, Fig. 5.25 | Equal when the lines are parallel |
| Interior angles on the same side | Between the two lines, same side of the transversal | ∠3 and ∠6, Fig. 5.28 | Sum = 180° when the lines are parallel |
| Drawing a parallel | Ruler and set square, or two paper folds | Fig. 5.21, Fig. 5.24 | Equal corresponding angles guarantee parallelism |
Exercises
- In-text Questions — Across the Line Page 106
- In-text Questions — Across the Line Page 107
- Figure it Out — Across the Line Page 108
- In-text Questions — Perpendicular Lines Page 108
- In-text Questions — Between Lines Page 109
- In-text Questions — Between Lines Page 110
- Activity 2 — Parallel and Perpendicular Lines in Paper Folding Page 111
- In-text Questions — Paper Folding, and Notations Page 112
- Figure it Out — Parallel and Perpendicular Lines in Paper Folding Page 113–114
- In-text Questions — Transversals and 5.6 Corresponding Angles Page 115
- Activity 3 — Corresponding Angles Page 116
- Activities 4 and 5 — Corresponding Angles Page 117
- In-text Questions — Drawing Parallel Lines Page 118–119
- Figure it Out — Drawing Parallel Lines Page 119
- In-text Questions — Alternate Angles Page 120
- Examples — Alternate Angles Page 120–122
- Figure it Out — Alternate Angles Page 123–125
- In-text Questions — Parallel Illusions Page 125