Question

Which among the following is not an example of postulate ?

• A. A straight line has one and only one midpoint.
• B. Angles opposite to equal sides of a De triangle are equal.
• C. Two straight lines cannot intersect in more than 1 point.
• D. A circle can be drawn with any point as centre and any length as radius.

Answer 1

Answer:

B. Angles opposite to equal sides of a De triangle are equal.

The statement "Angles opposite to equal sides of a Δ (triangle) are equal" is not an example of a postulate; it is actually a theorem.

A postulate is a fundamental assumption or axiom that is accepted without proof, while a theorem is a statement that is proven based on postulates, axioms, and previously established theorems.

The statement "Angles opposite to equal sides of a triangle are equal" is part of the properties of triangles and is proven using the axioms or postulates of geometry. It is known as the Base Angles Theorem or Isosceles Triangle Theorem.

In contrast, postulates are basic assumptions like:

• Through any two points, there is exactly one straight line.

• A straight line can be extended infinitely in both directions.

So, "Angles opposite to equal sides of a Δ are equal" is a theorem, not a postulate.