Which of the following needs a proof ?

Options

A. Theorems
B. Axiom
C. Definition
D. Postulate

Explanation

To determine which of the following needs a proof, we need to analyze each option:

1. **Theorem**: A theorem is a statement that has been proven based on previously established statements, such as other theorems, axioms, and definitions. Therefore, a theorem requires a proof.

2. **Definition**: A definition is a statement that explains the meaning of a term or concept. Definitions do not require proof because they are accepted as true by their nature.

3. **Postulate**: A postulate (or axiom) is a statement that is accepted as true without proof. Postulates serve as the foundational building blocks for further reasoning and proofs in geometry.

4. **Exam**: An exam is an assessment tool and does not pertain to mathematical statements that require proof.

Based on the analysis above, the only option that requires a proof is:

**Answer**: Theorem

### Step-by-Step Solution:
1. Identify the options: Theorem, Definition, Postulate, Exam.
2. Understand the meaning of each term:
- A theorem is a statement that requires proof.
- A definition explains a term and does not require proof.
- A postulate is an accepted truth without proof.
- An exam is an assessment and does not require proof.
3. Conclude that the only option that needs a proof is the theorem.