Question

a statement is given. \if a parallelogram is a square, then the parallelogram is a rhombus.\ complete the sentence to show whether the converse, contrapositive, or inverse is true and why. the dropdown is true because a parallelogram that dropdown is dropdown.

Explanation:

Step1: Recall definitions

• Original statement: \( p \to q \), where \( p \): "a parallelogram is a square", \( q \): "the parallelogram is a rhombus".
• Converse: \( q \to p \) (If a parallelogram is a rhombus, then it is a square).
• Contrapositive: \(

eg q \to
eg p \) (If a parallelogram is not a rhombus, then it is not a square).

• Inverse: \(

eg p \to
eg q \) (If a parallelogram is not a square, then it is not a rhombus).

Step2: Analyze each

• Converse: A rhombus has all sides equal but angles may not be right angles (so not all rhombuses are squares). So converse is false.
• Contrapositive: If a parallelogram is not a rhombus (does not have all sides equal), then it can't be a square (since square requires all sides equal). So if \(

eg q \) (not a rhombus), then \(
eg p \) (not a square) is true.

• Inverse: A parallelogram not a square can still be a rhombus (e.g., a rhombus with non - right angles). So inverse is false.

Answer:

The contrapositive is true because a parallelogram that is not a rhombus is not a square.