Class 9 Maths – Introduction to Euclid’s Geometry

5.1 Introduction

• Geometry studies the properties and relations of points, lines, surfaces, and solids.
• Euclid, an ancient Greek mathematician, is called the “Father of Geometry”.
• His work “Elements” (around 300 B.C.) is the foundation of modern geometry.

Key Idea: Euclid’s geometry is based on definitions, axioms, postulates, and theorems.

---

5.2 Euclid’s Definitions, Axioms, and Postulates

1. Definitions

Euclid began with basic terms and their meanings:

Term	Definition
Point	That which has no part, only position
Line	Breadthless length extending in two directions
Straight line	Line which lies equally in both directions
Surface	That which has length and breadth only
Plane surface	Surface which lies evenly on all sides
Angle	Inclination of two lines meeting at a point

---

2. Axioms (Common Notions)

• General truths accepted without proof.
• Examples:

1. Things equal to the same thing are equal to each other.
2. If equals are added to equals, the sums are equal.
3. The whole is greater than the part.

---

3. Postulates

• Statements accepted without proof specific to geometry.
• Euclid’s five postulates:

1. A straight line can be drawn joining any two points.
2. A straight line can be extended indefinitely in a straight line.
3. A circle can be drawn with any center and radius.
4. All right angles are equal.
5. Parallel Postulate: If a line falls on two lines and interior angles on the same side < 180°, the two lines meet on that side.

---

Quick Short Q&A (Most Possible)

Question	Short Answer
Who is Father of Geometry?	Euclid
Name of Euclid’s famous work?	Elements
Definition of a point?	That which has no part
Straight line?	Line which lies equally in both directions
What is an angle?	Inclination of two lines at a point
Axioms?	General truths without proof
Postulates?	Accepted statements in geometry
First Euclid’s postulate?	Line can be drawn joining two points
Fifth postulate?	Parallel postulate
Are right angles equal?	Yes