NCERT Solutions Class 9 Maths Chapter 5 — Introduction to Euclid's Geometry

Solution:

Step 1: Euclid defined a point as 'that which has no part'. This emphasizes its fundamental nature as a position without any dimension.

Step 2: Other options describe lines, magnitudes, or incorrectly attribute dimensions to a point.

Solution:

Step 1: Euclid's First Axiom (also known as a Common Notion) explicitly states: 'Things which are equal to the same thing are equal to one another'.

Step 2: This axiom is crucial for establishing equality in proofs and problem-solving.

Solution:

Step 1: The statement 'If equals are added to equals, the wholes are equal' is Euclid's Second Axiom (or Common Notion).

Step 2: Axioms are general truths that are accepted without proof and are applicable in all fields of mathematics, not just geometry. Postulates are specific to geometry.

Solution:

Step 1: Euclid's Postulate 1 states that 'A straight line may be drawn from any one point to any other point'.

Step 2: This postulate establishes the fundamental concept of connecting two points with a unique straight line.

Solution:

Step 1: A line segment is defined as a part of a line with two distinct end-points.

Step 2: Therefore, the statement 'A line segment has two end-points' is a definition, as it describes the fundamental property of a line segment.