Introduction
Euclid's Geometry is based on axioms, postulates, and theorems that describe the fundamental properties and relations of geometric figures.
Important Points
- Geometry is the study of shapes, sizes, and properties of space.
- Euclid is known as the 'Father of Geometry'.
- Euclid's Elements is one of the most influential works in mathematics.
- Axioms: General truths accepted without proof.
- Postulates: Geometrical statements accepted without proof.
Important Axioms & Postulates
1. Things which are equal to the same thing are equal to one another.
2. If equals are added to equals, the wholes are equal.
3. A straight line can be drawn from any point to any other point.
4. All right angles are equal to one another.
5. A circle can be drawn with any centre and radius.
Solved Examples
Example 1: State whether the statement "All right angles are equal" is an axiom or postulate.
Solution: It is a postulate.
Solution: It is a postulate.
Example 2: Which postulate allows us to draw a unique straight line through two points?
Solution: Euclid's First Postulate.
Solution: Euclid's First Postulate.
Example 3: If equals are subtracted from equals, the remainders are equal – Is it an axiom or postulate?
Solution: Axiom.
Solution: Axiom.
Example 4: Draw a circle with centre O and radius 5 cm. Which postulate is applied?
Solution: Postulate 3.
Solution: Postulate 3.
Example 5: Identify whether "A straight line can be produced indefinitely" is an axiom or postulate.
Solution: Postulate.
Solution: Postulate.
Practice Questions
- Name the book written by Euclid containing his work on geometry.
- Define an axiom with one example.
- State Euclid’s first postulate.
- Write any two axioms of Euclid.
- Explain the difference between axioms and postulates.