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JAC • Class 6 • Mathematics • Ch 10

Estimated Time: 45 Mins

Study Progress: In Progress

Pairs of Lines

Recognise intersecting, parallel, perpendicular and concurrent lines in everyday objects.

View All Chapters JCERT Hindi Textbook

Overview Core Concepts Solved Examples Common Traps Summary Self Check Take MCQ Test

Why This Chapter Matters

Recognise intersecting, parallel, perpendicular and concurrent lines in everyday objects.

Before You Begin (Prerequisites)

Familiarity with simple shapes and measurement

What You Will Learn (Core Objectives)

Recognise intersecting, parallel, perpendicular and concurrent lines in everyday objects.

Chapter Roadmap & Progression

1 Syllabus and book alignment

2 Concept 1

3 Concept 2

4 Concept 3

Complete Concept Guide (100% Curriculum Coverage)

Syllabus and book alignment

JCERT 2026–27: Regular schools (Non-SOE) — Chapter 10 · Pairs of Lines. Syllabus pages 180–185. These notes follow this topic. Official syllabus. Official JCERT Hindi textbook. Some source PDFs are damaged. The supplementary reference uses different chapter numbering.

Concept 1

Intersecting lines meet at a point. Two distinct straight lines in a plane cannot meet at two different points.

Concept 2

Parallel lines in the same plane never meet, even when extended. Perpendicular lines intersect at a right angle of 90°. All perpendicular lines intersect, but all intersecting lines are not perpendicular.

Concept 3

Three or more lines passing through the same point are concurrent. The common point is their point of concurrence. Railway tracks illustrate parallel lines; the adjacent edges of a rectangular notebook illustrate perpendicular lines.

Conceptual Solved Examples & Case Studies

Example 1

Two lines meet at 60°. Are they perpendicular?

Step-by-Step Solution:

They intersect, but they are not perpendicular because their angle is not 90°.

Common Misconceptions & Examiner Traps

Common Misconception

Common misconception

Scientific Reality & Correction

Do not decide parallelism from a short sketch alone; consider the lines extended in both directions.

Chapter Summary & 10 Key Takeaways

Takeaway 1

Intersecting lines meet at a point. Two distinct straight lines in a plane cannot meet at two different points.

Takeaway 2

Takeaway 3

Check Your Understanding (Diagnostic Practice Questions)

Diagnostic questions testing core conceptual clarity. Answers are hidden initially — solve each problem first, then click to reveal the step-by-step verified solution.

Three lines pass through point P. What are they called?

Reveal Answer & Explanation

Answer: Concurrent lines; P is the point of concurrence.
Use the definition above.

Chapter practice

CBT tests for this chapter are not published yet. Solve the self-check questions above and compare your answers.

All Class 6 Mathematics Chapters

Ch 1: Knowing Our Numbers Ch 2: Whole Numbers Ch 3: Integers Ch 4: Playing with Numbers Ch 5: Fractions Ch 6: Decimals Ch 7: Ratio and Proportion Ch 8: Algebra Ch 9: Line, Line Segment and Ray Ch 10: Pairs of Lines Ch 11: Angles Ch 12: Polygons Ch 13: Circle Ch 14: Three-Dimensional Shapes Ch 15: Symmetry Ch 16: Practical Geometry Ch 17: Perimeter and Area Ch 18: Data Handling

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