Intersecting and Parallel Lines
Look at the roads near your school. Some roads cross each other — those are like intersecting lines. Other roads run side by side without ever meeting — those are like parallel lines.
In geometry, understanding how lines relate to each other is very important. Lines can intersect (cross), be parallel (never meet), or be the same line (coincident).
In Class 6 NCERT Maths, you will learn about intersecting lines, parallel lines, and how to identify them in everyday life.
What is Intersecting and Parallel Lines - Grade 6 Maths (Basic Geometrical Ideas)?
- Two lines that cross each other at exactly one point are called intersecting lines.
- The point where they cross is called the point of intersection.
- At the point of intersection, four angles are formed.
- Two lines that are always the same distance apart and never meet, no matter how far they are extended, are called parallel lines.
- We write parallel lines as: line l || line m (the symbol || means "parallel to").
Intersecting and Parallel Lines Formula
How to identify:
- Intersecting lines meet at a point. The point of intersection can be found by extending the lines if needed.
- Parallel lines never meet. The distance between them stays the same everywhere.
- Perpendicular lines are a special case of intersecting lines where the angle at the point of intersection is 90° (a right angle).
Symbol:
- Parallel: l || m (l is parallel to m)
- Perpendicular: l ⊥ m (l is perpendicular to m)
Types and Properties
Types of line relationships:
- Intersecting lines: Meet at exactly one point. Example: The letter X is made of two intersecting lines.
- Perpendicular lines: Intersecting lines that make a 90° angle. Example: The corner of a book, the plus sign (+).
- Parallel lines: Never meet, always the same distance apart. Example: Railway tracks, opposite edges of a ruler.
- Concurrent lines: Three or more lines that all pass through the same point.
Important fact: In a flat surface (plane), two straight lines can either intersect at one point or be parallel. There is no other possibility. (They cannot intersect at two points.)
Solved Examples
Example 1: Identifying Intersecting Lines
Problem: Do the lines AB and CD intersect if A = (0,0), B = (4,4), C = (0,4), D = (4,0)?
Solution:
Line AB goes from bottom-left to top-right. Line CD goes from top-left to bottom-right.
They cross each other at the middle point (2, 2).
Answer: Yes, they are intersecting lines. Their point of intersection is (2, 2).
Example 2: Identifying Parallel Lines in Real Life
Problem: Give 5 examples of parallel lines from daily life.
Solution:
- Railway tracks
- Opposite edges of a notebook
- Horizontal lines on a ruled page
- Opposite sides of a rectangular door
- Lanes of a straight road
Example 3: Identifying Intersecting Lines in Real Life
Problem: Give 5 examples of intersecting lines from daily life.
Solution:
- Crossroads (two roads crossing each other)
- Scissors (two blades cross)
- The letter X
- Clock hands when they cross
- Two diagonals of a rectangle
Example 4: Parallel or Intersecting?
Problem: Look at the opposite edges of your textbook. Are they parallel or intersecting?
Solution:
The top edge and the bottom edge run in the same direction and are always the same distance apart. They never meet.
Answer: The opposite edges are parallel lines.
Example 5: Angles at Intersection
Problem: Two lines intersect. One of the angles formed is 60°. What are the other three angles?
Solution:
When two lines intersect, they form 4 angles. Vertically opposite angles are equal, and adjacent angles add up to 180°.
- Angle 1 = 60°
- Angle 2 (adjacent) = 180° − 60° = 120°
- Angle 3 (opposite to 1) = 60°
- Angle 4 (opposite to 2) = 120°
Answer: The four angles are 60°, 120°, 60°, 120°.
Example 6: Drawing Parallel Lines
Problem: How can you draw parallel lines using a ruler?
Solution:
- Draw a straight line using the ruler.
- Place the ruler at a fixed distance above (or below) the line.
- Draw another line along the ruler's edge.
- The two lines are parallel because they are the same distance apart everywhere.
Example 7: Lines on the Letter Z
Problem: In the letter Z, which lines are parallel and which are intersecting?
Solution:
The top horizontal line and the bottom horizontal line are parallel (both go left to right, never meeting).
The diagonal line intersects both horizontal lines, so it forms intersecting pairs with each of them.
Example 8: Can Lines Be Both?
Problem: Can two lines be both parallel and intersecting?
Solution:
No. Parallel lines never meet, and intersecting lines meet at a point. A pair of lines is either parallel or intersecting — never both.
Answer: No, a pair of lines cannot be both parallel and intersecting.
Real-World Applications
Real-life examples:
- Roads: Highway lanes are parallel. Crossroads are intersecting lines.
- Buildings: Floors of a building are parallel. A staircase intersects each floor.
- Sports: Goal posts are parallel vertical lines. The crossbar intersects them.
- Art and design: Artists use parallel and intersecting lines to create patterns and perspective drawings.
- Maps: Latitude lines are parallel to each other. Longitude lines intersect at the poles.
Key Points to Remember
- Intersecting lines meet at exactly one point (the point of intersection).
- Parallel lines never meet and are always the same distance apart.
- The symbol for parallel is ||.
- Perpendicular lines are intersecting lines that form a 90° angle.
- In a plane, two lines are either intersecting or parallel — no other option.
- When two lines intersect, they form 4 angles.
- Vertically opposite angles at an intersection are equal.
- Adjacent angles at an intersection add up to 180°.
Practice Problems
- Name 3 pairs of parallel lines in your classroom.
- Name 3 pairs of intersecting lines in your classroom.
- Two lines intersect making an angle of 75°. Find the other three angles.
- Are the two diagonals of a rectangle parallel or intersecting?
- Draw two parallel lines and one line that intersects both of them.
- Can three lines all be parallel to each other? Give an example.
Frequently Asked Questions
Q1. What are intersecting lines?
Intersecting lines are two lines that cross each other at exactly one point. That point is called the point of intersection. Example: the two diagonals of a square.
Q2. What are parallel lines?
Parallel lines are two lines that are always the same distance apart and never meet, no matter how far you extend them. Example: the two rails of a railway track.
Q3. What is the symbol for parallel?
The symbol is || (two vertical lines). We write l || m to mean line l is parallel to line m.
Q4. What are perpendicular lines?
Perpendicular lines are a special type of intersecting lines that meet at a right angle (90°). Example: the edges of a book cover at a corner.
Q5. Can two lines meet at more than one point?
No. Two distinct straight lines in a plane can meet at most at one point. If they meet at two points, they must be the same line (they overlap completely).
Q6. How do you check if two lines are parallel?
If the perpendicular distance between the two lines is the same everywhere, they are parallel. In a drawing, if they look like they go in the exact same direction without getting closer or farther apart, they are parallel.
Related Topics
- Point, Line Segment, Line and Ray
- Perpendicular Lines
- Types of Angles
- Transversal and Parallel Lines
- Collinear and Non-Collinear Points
- Curves - Open and Closed
- Introduction to Polygons
- Introduction to Triangles
- Quadrilateral Basics
- Circle - Basic Concepts
- Arc and Sector of a Circle
- Planes in Geometry
- Basic Geometrical Ideas
- Types of Lines
