Chapter 5 — Parallel and Intersecting Lines
Ganita Prakash • Grade 7 • Part I • 2026–27
📐 Geometry begins with relationships
Geometry is not only about naming shapes. It is about describing relationships precisely. In this chapter, students explore lines, intersections, angles and parallel lines through diagrams, constructions, paper-folding and reasoning.
1. Line, ray and line segment
| Object | Endpoints | Extent |
|---|---|---|
| Line | None | Extends in both directions |
| Ray | One | Extends in one direction |
| Line segment | Two | Fixed length |
2. Intersecting lines
When two lines meet, they intersect. Their meeting point is the point of intersection. Two intersecting lines form four angles. Opposite (vertically opposite) angles are equal. Adjacent angles on a straight line have a sum of 180°.
3. Parallel lines
Parallel lines in the same plane do not meet even when extended. Examples can be found in ruled lines and railway tracks, but a drawing alone is not a proof of parallelism.
4. A transversal
A line crossing two other lines is called a transversal. When the two lines are parallel, the angles created by the transversal show predictable relationships.
| Angle relationship | For parallel lines |
|---|---|
| Corresponding angles | Equal |
| Alternate interior angles | Equal |
| Interior angles on same side | Sum to 180° |
🧠 Worked Examples
- If one angle formed by two intersecting lines is 68°, its vertically opposite angle is 68°.
- Each adjacent angle is 180° − 68° = 112°.
- If a transversal crosses parallel lines and one corresponding angle is 75°, the corresponding angle is also 75°.
- If same-side interior angles are 110° and x°, then x = 180° − 110° = 70°.
🔍 Construction & Exploration
- Draw a line and mark a point outside it. Try constructing a line through the point parallel to the given line.
- Fold a sheet so two edges coincide and observe the angles formed.
- Draw two intersecting lines and measure all four angles. What pattern do you notice?
🎯 Reasoning Questions
- Why can we not prove two lines are parallel merely because they look parallel?
- If one angle at an intersection is 90°, what can you say about all four angles?
- Can two parallel lines have different lengths? Explain the distinction between a line and a segment.
🧩 Concept MCQs
- A ray has — A. one endpoint B. two endpoints C. no endpoints D. three endpoints
- Vertically opposite angles are — A. equal B. always 90° C. always 180° D. unequal
- For parallel lines cut by a transversal, corresponding angles are — A. equal B. always supplementary C. always 90° D. zero
- If one adjacent angle is 125°, the other is — A. 55° B. 65° C. 125° D. 45°
Answers: 1-A, 2-A, 3-A, 4-A
📌 Case-based Challenge
A road crosses two straight railway tracks. Assume the tracks are parallel and the road acts as a transversal. One angle at the first crossing is 72°.
- Find the corresponding angle at the second crossing.
- Find an adjacent angle at the first crossing.
- Explain which property you used in each answer.
- What would change if the tracks were not parallel?
🔥 Challenge Corner
Draw two lines that intersect at a point. Choose one angle. Can you determine all three remaining angles without measuring? Explain your reasoning.
📝 Worksheet
- Label line, ray and segment diagrams.
- Find unknown angles at intersections.
- Identify parallel lines and transversals.
- Solve corresponding/alternate/same-side angle problems.
- Write a reason beside every answer.