Which of the following needs a proof ?
a. Theorem
b. Axiom
c. Definition
d. Postulate

Solution:

We know that

Axiom, definition and postulate are self evident and no proof is required.

A proposition which requires a proof to establish the truth is a theorem.

Therefore, the theorem needs a proof.

✦ Try This: Playfair’s Axiom is an equivalent version of a. Euclid’s first postulate, b. Euclid’s second postulate, c. Euclid’s fourth postulate, d. Euclid’s fifth postulate

We know that

Playfair’s Axiom is an equivalent version of Euclid’s fifth postulate.

Therefore, it is an equivalent version of Euclid’s fifth postulate.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 5

NCERT Exemplar Class 9 Maths Exercise 5.1 Problem 20

Which of the following needs a proof ? a. Theorem, b. Axiom, c. Definition, d. Postulate

Summary:

A theorem is a mathematical statement whose truth has been logically established. Theorem needs a proof

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