The diagonals of a rhombus are perpendicular. The contrapositive of the above statement is

• If the figure is not a rhombus, then its diagonals are not perpendicular.
• If the diagonals are perpendicular, then the figure is a rhombus.
• If the diagonals are not perpendicular, then the figure is a rhombus.
• If the diagonals are not perpendicular, then the figure is not a rhombus.

The statement about the diagonals of a rhombus being perpendicular is an important property in geometry. Let's break down the contrapositive and related statements for clarity.

Understanding the Contrapositive

The contrapositive of a statement is formed by negating both the hypothesis and the conclusion, and then swapping them. For the original statement, "If a figure is a rhombus, then its diagonals are perpendicular," the contrapositive is:

• If the figure is not a rhombus, then its diagonals are not perpendicular.

Analyzing Related Statements

Now, let's look at the other statements you mentioned:

• If the diagonals are perpendicular, then the figure is a rhombus. This statement is not necessarily true, as other shapes can also have perpendicular diagonals.
• If the diagonals are not perpendicular, then the figure is a rhombus. This statement is false; a rhombus must have perpendicular diagonals.
• If the diagonals are not perpendicular, then the figure is not a rhombus. This statement is true, as it aligns with the property of rhombuses.

Summary of Key Points

In summary, the contrapositive correctly reflects the relationship between being a rhombus and having perpendicular diagonals. The other statements vary in truthfulness, with the last one being accurate. Understanding these relationships helps in grasping the properties of geometric figures.