Consider the following statement:
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram"
This statement is a/an

Options

A. axiom
B. proposition
C. definition
D. theorem

Answer

To determine the nature of the statement "If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram," we will analyze the options provided:

1. **Understanding the Statement**:
- The statement presents a condition (diagonals bisecting each other) and a conclusion (the quadrilateral is a parallelogram).

2. **Identifying the Type of Statement**:
- A **proposition** is a statement that can be either true or false.
- A **definition** is a statement that explains the meaning of a term or concept.
- A **theorem** is a statement that has been proven based on previously established statements, such as other theorems or axioms.
- A **corollary** is a statement that follows readily from a previously proven statement.

3. **Analyzing the Given Statement**:
- The statement is conditional and asserts a specific property of quadrilaterals based on the behavior of their diagonals.
- It is not merely defining a term, nor is it a proven theorem, as it requires proof to establish its truth.

4. **Conclusion**:
- Since the statement is a conditional assertion that can be tested for truth or falsity, it is best classified as a **proposition**.

Thus, the answer is **Option B: Proposition**.