Question

rewrite the definition of the term as a biconditional statement. (see example 5.)

1. the midpoint of a segment is the point that divides the segment into two congruent segments.

1. adjacent angles are two angles that share a common vertex and side but have no common interior points.

rewrite the statements as a single biconditional statement. (see example 5.)

1. if a polygon has three sides, then it is a triangle.

if a polygon is a triangle, then it has three sides.

Explanation:

Step1: Define biconditional structure

A biconditional combines a definition/conditional and its converse using "if and only if".

Step2: Rewrite 29 as biconditional

Combine the definition and its reverse.
A point is the midpoint of a segment if and only if it divides the segment into two congruent segments.

Step3: Rewrite 31 as biconditional

Combine the definition and its reverse.
Two angles are adjacent angles if and only if they share a common vertex and side but have no common interior points.

Step4: Rewrite 33 as biconditional

Merge the two given conditionals.
A polygon is a triangle if and only if it has three sides.

Answer:

1. A point is the midpoint of a segment if and only if it divides the segment into two congruent segments.
2. Two angles are adjacent angles if and only if they share a common vertex and side but have no common interior points.
3. A polygon is a triangle if and only if it has three sides.