Class 7 Maths Ch 5: Parallel and Intersecting Lines – learn intersecting, linear pair, vertically opposite, perpendicular and parallel lines with intuitive activities, notes, solved examples and quiz for CBSE Exam
Complete Chapter 5 guide: understanding lines on a plane (tables, paper, boards), intersecting lines and the four angles they form, linear pairs that sum to 180° and vertically opposite angles that are always equal, perpendicular lines forming right angles, and parallel lines that never meet, with hands‑on paper‑folding activities, real‑life examples, reasoning‑based “proof” ideas and practice questions for CBSE Class 7 Maths
Updated: 5 months ago
Categories: Class 7 Mathematics, NCERT Maths Notes 2025, Geometry Basics, Lines and Angles, CBSE Exam Preparation, Practice Questions & Quizze
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Class 7 Mathematics Chapter 5: Parallel and Intersecting Lines – Complete Notes, Solutions, Questions & Answers 2025
Chapter at a Glance – Parallel and Intersecting Lines
This chapter explores the relationships between lines on a plane surface, including intersecting lines, parallel lines, perpendicular lines, and the properties of angles formed by transversals.
Main Topics Covered
Intersecting lines and angles formed
Vertically opposite angles and linear pairs
Perpendicular lines (lines meeting at 90°)
Parallel lines (lines that never meet)
Transversals and the angles they form
Corresponding angles with parallel lines
Alternate angles with parallel lines
Interior angles on the same side of transversal
Drawing parallel lines using set squares
Key Takeaways for Exams
Vertically Opposite Angles
Always equal when two lines intersect.
Linear Pairs
Adjacent angles that add up to 180°.
Perpendicular Lines
Intersect at 90° (right angles).
Parallel Lines
Never meet, lie on same plane.
Corresponding Angles
Equal when transversal crosses parallel lines.
Alternate Angles
Equal when transversal crosses parallel lines.
Key Concepts & Rules – Parallel and Intersecting Lines
Important definitions, properties of angles, and rules for parallel lines for quick reference.
Key Rules
Intersecting Lines: Two lines that meet at a point form 4 angles.
Vertically Opposite Angles: Always equal to each other.
Linear Pair: Adjacent angles formed by intersecting lines; sum = 180°.
Perpendicular Lines: Intersect at 90°; all four angles are right angles.
Parallel Lines: Lines on same plane that never intersect.
Transversal: A line that intersects two or more lines.
Corresponding Angles: Equal if lines are parallel.
Alternate Angles: Equal if lines are parallel.
Interior Angles (Same Side): Sum = 180° if lines are parallel.
Angle Relationships
Angle Type
Property
Condition
Vertically Opposite
Equal
Any intersecting lines
Linear Pair
Sum = 180°
Adjacent angles on a line
Corresponding
Equal
Transversal on parallel lines
Alternate
Equal
Transversal on parallel lines
Interior (Same Side)
Sum = 180°
Transversal on parallel lines
Golden Lines for Exams
"When corresponding angles are equal, lines are parallel; When lines are parallel, corresponding and alternate angles are equal."
Concept Cards – Quick Explanations
Intersecting Lines
Two lines meeting at a point form 4 angles.
Exam Tip: Check vertically opposite angles are equal.
Vertically Opposite Angles
Opposite angles formed by intersecting lines are always equal.
Linear Pairs
Adjacent angles on a straight line always sum to 180°.
Perpendicular Lines
Lines intersecting at 90°; all four angles are right angles.
Parallel Lines
Lines that never meet on a plane surface.
Transversal
A line crossing two or more lines, forming 8 angles.
Corresponding Angles
In same position at each intersection; equal if parallel.
Alternate Angles
On opposite sides of transversal; equal if parallel.
Examples + Solutions
Example 1: Finding Angles with Intersecting Lines
Problem: Two lines intersect. If one angle is 120°, find all other angles.
Solution:
Let ∠a = 120°
∠b = 180° - 120° = 60° (linear pair)
∠c = 120° (vertically opposite to ∠a)
∠d = 60° (vertically opposite to ∠b)
Answer: The four angles are 120°, 60°, 120°, 60°.
Example 2: Parallel Lines and Transversal (from textbook)
Problem: Parallel lines l and m are intersected by transversal t. If ∠6 = 135°, find all other angles.
