Chapter 5
Parallel and Intersecting Lines
Learn the concept of lines, line segments, rays, parallel lines, intersecting lines, transversals and angles through colourful illustrations, real-life examples, solved examples and practice questions.
Study Time
2–3 Hours
Difficulty
Easy
Topics
8 Major Topics
Practice MCQs
50+ Questions
Learning Progress
Complete every topic to achieve 100% mastery.
Topics Covered
🎯 Learning Outcomes
After studying this chapter, students will be able to:
- Understand what a line is.
- Differentiate between line, ray and line segment.
- Identify parallel lines.
- Recognise intersecting lines.
- Understand transversals.
- Identify different types of angles.
- Apply concepts in daily life.
- Solve NCERT exercise questions confidently.
📘 Introduction
Whenever we look around us, we can see many different kinds of lines. Roads, railway tracks, electric wires, bridges, doors, windows, notebooks and buildings all contain lines. Some lines never meet, whereas some lines cross each other. Mathematics studies these relationships carefully. In this chapter we shall learn about parallel lines, intersecting lines, transversals and angles formed by them. These concepts are used in engineering, architecture, road construction, mapping and computer graphics.
🌍 Real-Life Examples
Railway Tracks
Two railway tracks always remain parallel.
Road Crossing
Two roads crossing each other form intersecting lines.
Buildings
Edges of walls are parallel.
Notebook
The ruled lines in notebooks are parallel.
💡 Did You Know?
Parallel railway tracks appear to meet at a distance, but actually they never intersect. This happens because of perspective.
📝 Warm-up Activity
Look around your classroom and identify:
- Five examples of parallel lines.
- Three examples of intersecting lines.
- One example of a transversal.
📌 Quick Recap
- Lines are everywhere around us.
- Some lines never meet.
- Some lines intersect.
- Parallel lines always remain the same distance apart.
- Intersecting lines meet at one point.
📏 What is a Line?
A line is a straight path that extends endlessly in both directions. It has no starting point and no ending point.
Representation of a Line
←────────────────────────────→
Line AB
The arrows at both ends show that the line continues forever.
📐 Line Segment
A line segment has two fixed end points. Unlike a line, its length can be measured.
Line Segment AB
A ●────────────● B
Characteristics
- Has two endpoints.
- Has fixed length.
- Can be measured.
- Written as AB.
☀ Ray
A ray starts from one point and extends endlessly in one direction.
Ray AB
A ●──────────────→
- One starting point.
- No ending point.
- Extends infinitely in one direction.
📊 Difference between Line, Ray and Line Segment
| Feature | Line | Ray | Line Segment |
|---|---|---|---|
| End Points | None | One | Two |
| Length | Infinite | Infinite | Fixed |
| Can Measure? | No | No | Yes |
| Direction | Both | One | None |
🟦 Parallel Lines
Two lines are called parallel lines if they remain the same distance apart and never meet even when extended infinitely.
Parallel Lines
──────────────────────── ────────────────────────
Examples
✖ Intersecting Lines
When two lines meet at one point, they are called intersecting lines.
Intersecting Lines
\ /
\ /
\ /
\ /
X
/ \
/ \
/ \
/ \
Examples
🎯 Classroom Activity
Observe your classroom and identify:
- 5 examples of parallel lines.
- 5 examples of intersecting lines.
- One line segment.
- One ray.
⭐ Key Points
- A line extends endlessly in both directions.
- A ray has one endpoint.
- A line segment has two endpoints.
- Parallel lines never meet.
- Intersecting lines meet at one point.
- Railway tracks are examples of parallel lines.
- Scissors show intersecting lines.
📝 Quick Check
- Can parallel lines meet?
- Which has two endpoints?
- Which figure has one endpoint?
- Give two examples of intersecting lines.
- Can we measure the length of a line?
🔷 Transversal
A transversal is a line that cuts two or more lines at different points. When a transversal intersects two parallel lines, many important angle relationships are formed.
Transversal Cutting Two Parallel Lines
───────────────
/
/
─────/─────────
📐 Angles Formed by Intersecting Lines
Whenever two lines intersect, they form four angles. Some of these angles are equal while others add up to 180°.
1
\
2 ------X------ 4
/
3
- Four angles are formed.
- Opposite angles are equal.
- Adjacent angles form a straight angle.
🔄 Vertically Opposite Angles
When two lines intersect, the angles opposite each other are called Vertically Opposite Angles.
∠2 = ∠4
Example
If one angle measures 70°, its vertically opposite angle is also 70°.
📏 Linear Pair
Two adjacent angles whose non-common arms form a straight line are called a Linear Pair.
──────────────
/
/
Angle A + Angle B = 180°
⭐ Important Properties
Property 1
Vertically opposite angles are always equal.
Property 2
Angles in a linear pair always add up to 180°.
Property 3
Two intersecting lines always form four angles.
Property 4
Parallel lines never meet, even if extended forever.
✅ Solved Example 1
One angle formed by two intersecting lines is 65°. Find the remaining angles.
- Vertically opposite angle = 65°
- Adjacent angles = 180° − 65° = 115°
✅ Solved Example 2
Two lines intersect. If one angle is 120°, find the other three angles.
- Opposite angle = 120°
- Adjacent angles = 180° − 120° = 60°
🌍 Real-Life Applications
💡 Remember
- Vertically opposite angles are equal.
- Linear pair angles always total 180°.
- Parallel lines never intersect.
- A transversal cuts two or more lines.
📝 Practice Questions
- Define a transversal.
- How many angles are formed when two lines intersect?
- State the property of vertically opposite angles.
- What is a linear pair?
- If one angle is 45°, find the remaining three angles.
- If one angle is 135°, find all other angles.
- Can parallel lines intersect? Explain.
- Give three real-life examples of intersecting lines.
- What is the sum of a linear pair?
- Why are railway tracks parallel?
📌 Chapter Summary
- A transversal intersects two or more lines.
- Intersecting lines form four angles.
- Vertically opposite angles are equal.
- Angles in a linear pair add up to 180°.
- These concepts are widely used in engineering, architecture, road design, and geometry.
📚 NCERT Exercise Solutions
Practice the following NCERT-style questions before checking the answers.
Question 1
What are parallel lines?
Question 2
What are intersecting lines?
Question 3
State one example of parallel lines from daily life.
Question 4
State one example of intersecting lines.
❓ Practice MCQs
1. Parallel lines always
A) Meet
B) Never meet ✅
C) Form circles
D) Bend
2. Intersecting lines meet at
A) Two points
B) One point ✅
C) Three points
D) No point
3. Railway tracks are
A) Curved
B) Parallel ✅
C) Zig-zag
D) Intersecting
4. Notebook ruled lines are
A) Parallel ✅
B) Intersecting
C) Rays
D) Segments
5. Vertically opposite angles are
A) Unequal
B) Equal ✅
C) Zero
D) Random
6. Sum of a linear pair equals
A) 90°
B) 180° ✅
C) 360°
D) 45°
7. A line has
A) Two endpoints
B) One endpoint
C) No endpoints ✅
D) Four endpoints
8. A ray has
A) No endpoint
B) One endpoint ✅
C) Two endpoints
D) Infinite endpoints
9. A line segment has
A) One endpoint
B) Two endpoints ✅
C) No endpoint
D) Infinite endpoints
10. Which is NOT parallel?
A) Railway tracks
B) Notebook lines
C) Road crossing ✅
D) Window grills
✔ True / False
- Parallel lines intersect. False
- Intersecting lines meet at one point. True
- A line segment has fixed length. True
- A ray has two endpoints. False
- Vertically opposite angles are equal. True
📝 Fill in the Blanks
- Two lines meeting at one point are ________. (Intersecting)
- Railway tracks are ________. (Parallel)
- A ray has ______ endpoint. (One)
- A line has ______ endpoints. (No)
- Angles in a linear pair sum to ______°. (180)
✍ Short Answer Questions
- Define parallel lines.
- Define intersecting lines.
- What is a transversal?
- State one property of vertically opposite angles.
- Give two examples of parallel lines.
📖 Long Answer Questions
- Differentiate between line, ray and line segment with examples.
- Explain parallel and intersecting lines using suitable diagrams.
- Describe vertically opposite angles with examples.
- Explain linear pair with illustration.
- Write five real-life applications of parallel lines.
🚀 HOTS Questions
- Can two curved lines be parallel? Explain.
- Why do railway tracks appear to meet at a distance?
- Can two intersecting lines become parallel? Why?
- Explain the importance of parallel lines in architecture.
- Where do we use intersecting lines in engineering?
📄 Case Study
Rahul is travelling by train. He observes two railway tracks that remain the same distance apart throughout the journey.
Answer the following:- What type of lines are these?
- Do they ever meet?
- Give another real-life example.
- Why is equal distance important?
🎯 Exam Tips
- Learn all definitions exactly.
- Remember the properties of parallel lines.
- Practice diagrams neatly.
- Revise angle properties.
- Solve NCERT questions first.
📖 Quick Revision Notes
📏 Line
A line extends endlessly in both directions.
📐 Line Segment
Has two endpoints and fixed length.
☀ Ray
Starts at one point and extends endlessly in one direction.
🟦 Parallel Lines
Remain the same distance apart and never meet.
✖ Intersecting Lines
Meet at exactly one point.
🔷 Transversal
Cuts two or more lines at different points.
⭐ Important Facts
🧠 Chapter Mind Map
💡 Memory Tricks
- 🚆 Railway Tracks → Parallel Lines
- ✂ Scissors → Intersecting Lines
- 📖 Notebook → Parallel Lines
- 🕒 Clock Hands → Intersecting Lines
- ➕ Crossroads → Intersecting Lines
⚠ Common Mistakes
- Do not confuse a Line with a Line Segment.
- Remember that a Ray has only one endpoint.
- Parallel lines never meet.
- Vertically opposite angles are equal.
- Linear Pair always equals 180°.
📥 Download Chapter Resources
🎥 Video Tutorials
Parallel Lines Explained
Intersecting Lines
Angles Practice
📚 Related Chapters
❓ Frequently Asked Questions
1. Can parallel lines ever meet?
No. They remain at a constant distance forever.
2. What is an intersecting line?
Two lines meeting at one point.
3. Where are parallel lines used?
Railway tracks, roads, bridges, buildings, engineering and architecture.
4. What is a transversal?
A line that cuts two or more lines.
🎉 Congratulations!
You have successfully completed Chapter 5 — Parallel and Intersecting Lines