Parallel and Intersecting Lines - Class 7 Mathematics (CBSE)

Based on the 2026-27 Class 7 Mathematics sequence for NCERT Ganita Prakash. These notes are written for students: understand the idea first, then practise enough examples to become accurate.

1. Why this chapter matters

Roads, railway tracks, notebook margins, window grills, and floor tiles all show relationships between lines. This chapter teaches students to recognise when lines meet, never meet, or are cut by another line, and to use angle facts instead of guessing by sight.

In school tests, this chapter can appear as direct calculations, reasoning questions, short explanations, activity-based questions, and word problems. The safest preparation is not to memorise a single trick, but to know what each idea means and when to use it.

2. Core ideas

Parallel lines

Lines in the same plane that never meet are parallel. They remain the same distance apart everywhere.

Intersecting lines

Lines that meet at one point are intersecting lines. The meeting point creates angles.

Transversal

A transversal is a line that cuts two or more lines. When it cuts parallel lines, many angle relationships appear.

3. Rules and formulas to remember

• Vertically opposite angles: Equal. Formed when two lines intersect.
• Linear pair: Sum = 180 degrees. Adjacent angles on a straight line.
• Corresponding angles: Equal for parallel lines. When a transversal cuts parallel lines.
• Alternate interior angles: Equal for parallel lines. Angles inside the parallel lines on opposite sides of transversal.

4. Worked examples

Example 1: Two lines intersect. One angle is 65 degrees. Find the vertically opposite angle.

Vertically opposite angles are equal, so the angle is 65 degrees.

Example 2: An angle forms a linear pair with 112 degrees. Find it.

Linear pair sum = 180 degrees. Required angle = 180 - 112 = 68 degrees.

Example 3: A transversal cuts parallel lines. One corresponding angle is 74 degrees. Find the matching corresponding angle.

Corresponding angles are equal, so it is 74 degrees.

Example 4: Why are railway tracks modelled as parallel lines?

They must remain the same distance apart and should not meet.

5. Activity corner

Draw two parallel lines and cut them with a transversal. Use tracing paper to compare corresponding and alternate interior angles. This makes the equality visible before students memorise names.

When writing an activity answer, include three things:

• What you did.
• What you observed.
• What mathematical rule or pattern the activity shows.

6. Common mistakes and how to avoid them

• Mistake: Judging parallel lines only by appearance Fix: Use constant distance or angle facts, not just eyesight.
• Mistake: Confusing alternate and corresponding angles Fix: Mark the transversal and locate whether angles are on the same relative corner or opposite inside corners.
• Mistake: Forgetting that a straight angle is 180 degrees Fix: Every linear pair rests on this fact.

7. How to write high-scoring answers

1. State the given information in mathematical form.
2. Write the rule, formula, diagram, table, or operation you are using.
3. Show every step clearly.
4. Keep units such as cm, m, rupees, degrees, or minutes where needed.
5. Check whether the answer is reasonable.

8. Practice set

1. Define parallel lines.
2. Find the supplement of 47 degrees.
3. If vertically opposite angles are x and 83 degrees, find x.
4. Name one real-life example of intersecting lines.
5. What is a transversal?
6. Why are angle facts useful?

9. Answer key

1. Define parallel lines. Answer: Lines in the same plane that never meet.

2. Find the supplement of 47 degrees. Answer: 133 degrees.

3. If vertically opposite angles are x and 83 degrees, find x. Answer: 83 degrees.

4. Name one real-life example of intersecting lines. Answer: Scissors, crossing roads, or two clock hands.

5. What is a transversal? Answer: A line that intersects two or more lines.

6. Why are angle facts useful? Answer: They allow exact reasoning without measurement each time.

10. Quick revision

• Main themes: lines, parallel lines, intersecting lines, transversal, angles.
• Redo the worked examples without looking at the solutions.
• Explain the activity in your own words.
• Correct the common mistakes once before the test.
• Create one new word problem from daily life and solve it step by step.