PW Class 7 Maths Notes Chapter 5: Parallel and Intersecting Lines

Understanding how lines and angles are related is an important part of geometry. Whether you are identifying parallel roads, the corners of a notebook, or the angles formed when two lines meet, recognising these relationships helps you solve many geometry questions. However, remembering different angle pairs and their properties can often become confusing.

PW Class 7 Maths Chapter 5 Notes organise the complete chapter into simple definitions, rules, tables, and examples. These notes help you revise parallel lines, intersecting lines, transversals, and angle relationships before practising NCERT exercises or preparing for school assessments.

What Is the Difference Between a Line and a Line Segment?

A line is a straight path that extends endlessly in both directions, while a line segment is a part of a line with two fixed endpoints.

What Are Intersecting Lines?

Two lines that meet at a common point are called intersecting lines.

When two lines intersect:

• They form four angles.

• Opposite angles are called vertically opposite angles.

• Adjacent angles form a linear pair.

What Are Vertically Opposite Angles?

Vertically opposite angles are the angles directly opposite each other when two lines intersect.

Important Property

• Opposite angles are always equal.

• ∠a = ∠b

• ∠c = ∠d

This property helps you find unknown angles in geometry problems.

What Is a Linear Pair?

A linear pair consists of two adjacent angles formed on a straight line.

Linear Pair Rule

The sum of adjacent angles is always:

180∘180^\circ180∘

Examples:

• ∠1 + ∠2 = 180°

• ∠2 + ∠3 = 180°

• ∠3 + ∠4 = 180°

• ∠4 + ∠1 = 180°

Whenever two angles lie on the same straight line, they form a linear pair.

What Are Perpendicular Lines?

Perpendicular lines are intersecting lines that meet at a right angle.

Properties of Perpendicular Lines

• They intersect at exactly one point.

• The angle between them is 90°.

• They are represented using the symbol ⊥.

Example: If line XY is perpendicular to line AB, then XY ⊥ AB.

How Does Paper Folding Show Parallel and Perpendicular Lines?

A rectangular sheet of paper is a simple example of line relationships.

• Opposite sides are parallel.

• Adjacent sides are perpendicular.

• Every horizontal fold creates additional parallel fold lines.

Pattern of Parallel Lines

General Rule

The number of parallel lines after n folds is: 2n+1

What Is a Transversal?

A transversal is a line that intersects two or more lines at different points. A transversal creates several angle pairs, and their relationships become important when the lines are parallel.

How Are Interior and Exterior Angles Identified?

When a transversal intersects two parallel lines, the angles are classified as interior or exterior based on their position.

Interior angles are located inside the parallel lines, while exterior angles are formed outside them.

How Do Corresponding Angles Form?

Corresponding angles are the angles that occupy the same relative position on the same side of a transversal.

Corresponding Angle Pairs

Rule: When a transversal cuts two parallel lines, each pair of corresponding angles is equal.

What Are Alternate Interior and Alternate Exterior Angles?

Alternate angles lie on opposite sides of the transversal.

Alternate Interior Angles

• ∠3 and ∠5

• ∠4 and ∠6

Property: Alternate interior angles are equal.

Alternate Exterior Angles

• ∠1 and ∠7

• ∠2 and ∠8

Property: Alternate exterior angles are also equal.

What Are Consecutive (Co-Interior) Angles?

Consecutive angles are the interior angles on the same side of a transversal.

Co-Interior Angle Pairs

• ∠3 and ∠6

• ∠4 and ∠5

Important Rule

Their sum is always:

180∘

These are also called co-interior angles.

Class 7 Maths Chapter 5 Notes PDF

Use the Parallel and Intersecting Lines Chapter 5 Notes PDF to revise line types, transversals, and important angle relationships for quick revision.

What Makes PW Notes Useful for Class 7 Maths Chapter 5?

PW Chapter 5 Notes help you revise the complete chapter by bringing important geometry concepts, angle properties, and transversal rules together in one organised resource. They are designed to make revision quicker and concept learning easier.

• Revise Line Concepts: Understand lines, line segments, intersecting lines, and perpendicular lines with clear definitions.

• Learn Angle Properties: Quickly revise vertically opposite angles and linear pairs along with their important rules.

• Understand Transversals: Study interior, exterior, corresponding, alternate, and co-interior angles in a simple sequence.

• Strengthen Geometry Skills: Learn how parallel and perpendicular lines appear in paper folding and everyday geometric shapes.

• Remember Key Relationships: Recall the 90° and 180° angle rules commonly used in angle-based questions.

• Practise with Confidence: Use the notes to refresh concepts before solving NCERT exercises, important questions, and school assessments.

• Quick Chapter Revision: Revisit important definitions, examples, and properties without reading the complete lesson again.

Parallel and Intersecting Lines introduces the fundamental relationships between lines and angles in geometry. By understanding vertically opposite angles, linear pairs, transversals, corresponding angles, alternate angles, and co-interior angles, you can solve angle-based problems with greater accuracy. PW Class 7 Maths Chapter 5 Notes help you revise these concepts quickly and build a stronger foundation for geometry.

Related Resources

• CBSE Class 7 Maths NCERT Solutions

• CBSE Class 7 Maths Sample Papers

• CBSE Class 7 Maths Most Important Questions

• CBSE Class 7 Maths Notes