Notes Maths Class 7 Chapter 5 Ganita Prakash

Notes For All Chapters – Ganita Prakash Class 7th

Parallel and Intersecting Lines

1. Lines on a Plane

A line is straight and goes on forever in both directions.

Plane surface: Flat surface like a table, blackboard, or paper.

2. Intersecting Lines

When two lines meet at a point, they are called intersecting lines.

At the point of intersection, 4 angles are formed.

Key Properties:

Linear pair: Two adjacent angles on a straight line; their sum is 180°.

Vertically opposite angles: Angles opposite each other when lines intersect; they are equal.

Example:

If ∠a = 120°, then:
∠b = 60° (linear pair),
∠c = 120°,
∠d = 60°
⇒ ∠a = ∠c and ∠b = ∠d

3. Perpendicular Lines

Two lines intersecting at 90° (right angle) are called perpendicular lines.

Each of the 4 angles formed is 90°.

4. Parallel Lines

Lines that:

• Lie on the same plane.
• Never meet, no matter how far extended.

Example: Opposite edges of a square or the railway tracks.

In Notation:

Parallel lines are shown with arrows: l || m.

5. Transversal

A transversal is a line that cuts across two or more lines.

When it crosses two lines, 8 angles are formed.

6. Corresponding Angles

Formed when a transversal cuts two lines.

Angles in the same relative position.

Example pairs: ∠1 and ∠5, ∠2 and ∠6

Property:

• If the lines are parallel, corresponding angles are equal.
• If corresponding angles are equal, the lines must be parallel.

7. Alternate Angles

Alternate interior angles are formed inside two lines on opposite sides of the transversal.

Example: ∠c and ∠e in a ‘Z’ shape.

Property:

• If the lines are parallel, alternate angles are equal.

8. Interior Angles on Same Side

Also called co-interior angles.

Located on the same side of the transversal between the two lines.

Property:

• If lines are parallel, the sum of these angles is 180°.

9. Drawing Parallel Lines

Using Geometry Tools:

• Use set squares or protractor to ensure same angle with a transversal (e.g., both 90°).
• If corresponding angles formed are equal → lines are parallel.

Using Paper Folding:

• Fold to make a perpendicular.
• Fold again from that line to make another perpendicular.
• The new line is parallel to the first line.