Class 7 Maths Chapter 5 Parallel and Intersecting Lines NCERT Solutions (Step-by-Step Answers, Concepts & Examples | Ganita Prakash)
Class 7 Maths Chapter 5 Parallel and Intersecting Lines NCERT Solutions (Step-by-Step Answers, Concepts & Examples | Ganita Prakash)
Introduction
Lines are an important part of geometry. In everyday life we see many examples of lines:
• railway tracks
• roads
• edges of books
• window grills
Some lines meet each other, while others never meet even if extended infinitely.
When two lines meet, they form angles.
When they never meet, they are called parallel lines.
In this chapter students learn:
• Intersecting lines
• Parallel lines
• Transversal lines
• Different types of angles formed by intersecting lines
• Properties of angles formed by parallel lines
These ideas help build the foundation of geometry and algebra later in higher classes.
1. Intersecting Lines
Two lines that meet at a point are called intersecting lines.
Example:
Two roads crossing at a junction.
If line l and line m meet at point P, they are intersecting lines.
They form four angles around the point of intersection.
Illustration
Example diagram you can screenshot from the book:
Two straight lines crossing each other forming four angles.
Important Property
When two lines intersect:
Opposite angles are equal.
These angles are called vertically opposite angles.
Example:
If one angle is 60°
The vertically opposite angle is also 60°.
2. Vertically Opposite Angles
When two lines intersect, opposite angles are equal.
Example:
∠1 = ∠3
∠2 = ∠4
This property is called the Vertically Opposite Angle Theorem.
Example Question
Two lines intersect. One angle is 70°.
Find the vertically opposite angle.
Solution
Vertically opposite angles are equal.
Therefore
Angle = 70°
3. Adjacent Angles
Angles that share a common arm and vertex are called adjacent angles.
Example:
Two angles next to each other at the intersection point.
Property:
Adjacent angles on a straight line add up to 180°.
Example
If one angle is 110°, find the adjacent angle.
Solution
Angles on straight line = 180°
So,
Second angle =
180° − 110°
= 70°
4. Parallel Lines
Two lines that never meet even when extended infinitely are called parallel lines.
Symbol for parallel lines:
l ∥ m
Examples from daily life:
• railway tracks
• notebook lines
• opposite edges of a rectangle
These lines remain the same distance apart everywhere.
Illustration
Two horizontal lines that never intersect.
5. Transversal Line
A transversal is a line that cuts across two or more lines.
When a transversal cuts two parallel lines, several special angles are formed.
Example diagram:
Two parallel lines cut by a slanting line.
Types of Angles Formed
When a transversal cuts two parallel lines, we get:
• Corresponding angles
• Alternate interior angles
• Interior angles on the same side
6. Corresponding Angles
Angles that occupy the same relative position are called corresponding angles.
Property
If two parallel lines are cut by a transversal:
Corresponding angles are equal.
Example
∠1 = ∠5
∠2 = ∠6
∠3 = ∠7
∠4 = ∠8
Example Problem
If one corresponding angle is 65°, find the other.
Solution
Corresponding angles are equal.
Answer
65°
7. Alternate Interior Angles
Angles that lie between the two lines and on opposite sides of the transversal are called alternate interior angles.
Property
If lines are parallel:
Alternate interior angles are equal.
Example
∠3 = ∠6
∠4 = ∠5
Example Problem
Alternate interior angle = 80°
Find the corresponding alternate interior angle.
Answer
80°
8. Interior Angles on the Same Side
Angles that lie inside the parallel lines on the same side of transversal are called interior angles.
Property
These angles add up to 180°.
Example
∠3 + ∠5 = 180°
Example Question
If one interior angle is 120°, find the other.
Solution
Sum of interior angles = 180°
Second angle
= 180° − 120°
= 60°
Figure It Out – Example Question
Two parallel lines are cut by a transversal.
If one angle is 75°, find all other angles.
Step 1
Vertically opposite angle = 75°
Step 2
Adjacent angle =
180 − 75
= 105°
Step 3
Corresponding angle = 75°
Step 4
Alternate interior angle = 75°
Thus all angles become either 75° or 105°.
Key Concepts from Chapter
Students learned:
• Intersecting lines
• Vertically opposite angles
• Adjacent angles
• Parallel lines
• Transversal lines
• Corresponding angles
• Alternate interior angles
• Interior angles
These concepts form the basis of geometry and coordinate geometry in higher classes.
Practice Questions
Define intersecting lines.
If two lines intersect and one angle is 50°, find the vertically opposite angle.
Find the adjacent angle if one angle is 120°.
Define transversal.
What are corresponding angles?
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