Question

show that the definition is reversible. then write it as a true biconditional. 1. a quadrilateral is a polygon with four sides. conditional: converse: biconditional: 2. straight angles measure 180 degrees. conditional: converse: biconditional: 3. congruent angles are angles that have equal measures. conditional: converse: biconditional:

Explanation:

Step1: Recall conditional statement form

A conditional statement is of the form "if p, then q".

Step2: Find conditionals

For 1:

Conditional: If a polygon is a quadrilateral, then it has four sides.

For 2:

Conditional: If an angle is a straight - angle, then it measures 180 degrees.

For 3:

Conditional: If two angles are congruent, then they have equal measures.

Step3: Recall converse statement form

The converse of "if p, then q" is "if q, then p".

Step4: Find converses

For 1:

Converse: If a polygon has four sides, then it is a quadrilateral.

For 2:

Converse: If an angle measures 180 degrees, then it is a straight - angle.

For 3:

Converse: If two angles have equal measures, then they are congruent.

Step5: Recall biconditional statement form

A biconditional statement is of the form "p if and only if q" when the conditional and its converse are both true.

Step6: Find biconditionals

For 1:

Biconditional: A polygon is a quadrilateral if and only if it has four sides.

For 2:

Biconditional: An angle is a straight - angle if and only if it measures 180 degrees.

For 3:

Biconditional: Two angles are congruent if and only if they have equal measures.

Answer:

1.
Conditional: If a polygon is a quadrilateral, then it has four sides.
Converse: If a polygon has four sides, then it is a quadrilateral.
Biconditional: A polygon is a quadrilateral if and only if it has four sides.
2.
Conditional: If an angle is a straight - angle, then it measures 180 degrees.
Converse: If an angle measures 180 degrees, then it is a straight - angle.
Biconditional: An angle is a straight - angle if and only if it measures 180 degrees.
3.
Conditional: If two angles are congruent, then they have equal measures.
Converse: If two angles have equal measures, then they are congruent.
Biconditional: Two angles are congruent if and only if they have equal measures.