Question

1. first, write the following statement as an if - then statement, then write the converse, inverse, and contrapositive.

\all right angles are congruent\

1. first, write the following statement as an if - then statement, then write the converse, inverse, and contrapositive.

\any parallelogram has opposite angles congruent\

1. determine whether the following if - then statement is true in both directions. if it is, write as a biconditional, if not, explain.

\if a figure is a square, then it has four right angles.\

Explanation:

Step1: Rewrite statements for 1

If - then statement

If an angle is a right - angle, then it is congruent.

Converse

If an angle is congruent, then it is a right - angle.

Inverse

If an angle is not a right - angle, then it is not congruent.

Contrapositive

If an angle is not congruent, then it is not a right - angle.

Step2: Rewrite statements for 2

If - then statement

If a figure is a parallelogram, then it has opposite angles congruent.

Converse

If a figure has opposite angles congruent, then it is a parallelogram.

Inverse

If a figure is not a parallelogram, then it does not have opposite angles congruent.

Contrapositive

If a figure does not have opposite angles congruent, then it is not a parallelogram.

Step3: Analyze statement for 3

The original statement is "If a figure is a square, then it has four right angles". The converse is "If a figure has four right angles, then it is a square". A rectangle also has four right angles but is not a square. So the statement is not true in both directions.

Answer:

1.

• If - then: If an angle is a right - angle, then it is congruent.
• Converse: If an angle is congruent, then it is a right - angle.
• Inverse: If an angle is not a right - angle, then it is not congruent.
• Contrapositive: If an angle is not congruent, then it is not a right - angle.

2.

• If - then: If a figure is a parallelogram, then it has opposite angles congruent.
• Converse: If a figure has opposite angles congruent, then it is a parallelogram.
• Inverse: If a figure is not a parallelogram, then it does not have opposite angles congruent.
• Contrapositive: If a figure does not have opposite angles congruent, then it is not a parallelogram.

1. The statement "If a figure is a square, then it has four right angles" is not true in both directions because a rectangle has four right angles but is not a square.