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

Options

A. If the figure is not a rhombus, then its diagonals are not perpendicular .
B. If the diagonals are perpendicular,then the figure is a rhombus
C. If the digonals are not perpendicular, then the figure is a rhombus.
D. If the diagonals are not perpendicular, then the figure is not a rhombus

Explanation

To find the contrapositive of the statement "The diagonals of a rhombus are perpendicular," we can follow these steps:

### Step 1: Identify the original statement
The original statement can be expressed in an "if-then" form:
- If a figure is a rhombus (P), then its diagonals are perpendicular (Q).

### Step 2: Write the statement in symbolic form
We can denote the statement as:
- P → Q
Where P is "a figure is a rhombus" and Q is "its diagonals are perpendicular."

### Step 3: Formulate the contrapositive
The contrapositive of a statement P → Q is ¬Q → ¬P, where ¬ denotes negation.
- This means we need to negate both parts of the original statement:
- Negation of Q (¬Q): "The diagonals are not perpendicular."
- Negation of P (¬P): "The figure is not a rhombus."

### Step 4: Write the contrapositive in if-then form
Now we can write the contrapositive in if-then form:
- If the diagonals are not perpendicular (¬Q), then the figure is not a rhombus (¬P).

### Final Answer
Thus, the contrapositive of the statement "The diagonals of a rhombus are perpendicular" is:
- If the diagonals are not perpendicular, then the figure is not a rhombus.

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