Question

Rewrite the definition of the term as a logical a biconditional statement.

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

Answer 1

A logical biconditional statement for the definition of a midpoint is that M is the midpoint of AB iff AM and MB are congruent segments.

Step-by-step explanation:

The definition of a midpoint as a logical biconditional statement is: A point M is the midpoint of segment AB if and only if point M divides the segment AB into two congruent segments AM and MB. This can be mathematically symbolized as M is the midpoint of AB ↔ AM ≅ MB (where ↔ stands for 'if and only if' and ≅ stands for 'is congruent to').

This statement asserts two conditions that are true simultaneously: If M is the midpoint of AB, then AM and MB are congruent; and conversely, if AM and MB are congruent, then M must be the midpoint of AB. The Law of the Excluded Middle supports this logical structure by affirming that either this biconditional statement is true, or its negation is true, but not both.

Answer 2

The point is the midpoint of a segment if and only if it divides the segment into tow congruent segments.

Step-by-step explanation:

In writing a logical biconditional statement, you combine two conditional statements. In this case, both parts of the statements have the same truth value.

A biconditional statement is written as p q where "p if and only if q"

The p is the hypothesis in the statement and q is the conclusion.

In this cases,

p=The point is the midpoint of a segment, the hypothesis

q=it divides the segment into tow congruent segments, the conclusion.