## CBSE Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry Revision Notes

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## Euclid Geometry

Euclidean geometry is a mathematical system that is based on axioms and theorems employed by the Greek mathematician Euclid. He collected all the known work and arranged it in his famous treatise, called ‘Elements’, and divided the ‘Elements’ into thirteen chapters, each called a book. Euclid listed 23 definitions in book 1 of the ‘Elements’.

Axioms or postulates are the assumptions that are obvious universal truths. They are not proved. An axiom is a statement that is accepted to be true without proof. The assumptions that are specific to geometry are called postulates.

**Euclid’s Definitions:**

1. A point is that which has no part.

2. A line has no breadth but has length.

3. The ends of a line are points.

4. A straight line is a line which lies evenly with the points on itself.

5. A surface is that which has length and breadth only.

6. The edges of a surface are lines.

7. A plane surface is a surface which lies evenly with the straight lines on itself.

**Axioms:**

1. Things which are equal to the same things are also equal to one another.

2. If equals are added to equals, then the wholes are equal.

3. If equals are subtracted from equals, then the remainders are equal.

4. Things which coincide with one another are equal to one another.

5. The whole is greater than the part (universal truth).

6. Things which are double of the same things are equal to one another.

7. Things that are halves of the same things are equal to one another.

**Euclid’s Postulates:**

Postulate 1: A Straight line may be drawn from anyone point to any other point.

Postulate 2: A terminated line can be produced indefinitely.

Postulate 3: A circle can be drawn with any center and any radius.

Postulate 4: All right angles are equal to one another.

Postulate 5: If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

### CBSE Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry Revision Notes PDF