5. Test the following statement to see if it is reversible. If so, choose the true biconditional. A midpoint of a segment is a point that divides a segment into two congruent segments. If a point does not divide a segment into two congruent segments, it is not a midpoint. A point is a midpoint of a segment if and only if it divides the segment into two congruent segments. This statement is not reversible. A point that divides a segment into two congruent segments is a midpoint.
The statement is reversible and the true biconditional is: A point is a midpoint of a segment if and only if it divides the segment into two congruent segments.
To test if the statement is reversible, we need to determine if both the original statement and its converse are true.
The original statement: "A midpoint of a segment is a point that divides a segment into two congruent segments."
The converse of the statement: "A point that divides a segment into two congruent segments is a midpoint."
Let's test both statements:
1. If a point is a midpoint of a segment, then it divides the segment into two congruent segments.
This is true. By definition, a midpoint is a point that divides a segment into two congruent segments.
2. If a point divides a segment into two congruent segments, then it is a midpoint.
This is false. A point can divide a segment into two congruent segments without being the midpoint. For example, consider a line segment AB where point C divides it into two congruent segments AC and CB. Here, point C is not the midpoint of the segment AB.
Since the converse of the statement is false, the original statement is not reversible.
So, the true biconditional statement is: "A point is a midpoint of a segment if and only if it divides the segment into two congruent segments."
To test if a statement is reversible, we need to determine if both the original statement and its converse are true.
The original statement states that "A midpoint of a segment is a point that divides a segment into two congruent segments." Let's denote this as Statement A.
The converse of Statement A states "A point that divides a segment into two congruent segments is a midpoint." Let's denote this as Statement B.
To test for reversibility, we need to evaluate if both Statement A and Statement B are true.
First, we'll evaluate Statement A. To determine if a point is a midpoint, it must divide the segment into two congruent segments. If this condition is satisfied, then we can say that Statement A is true.
Next, we'll evaluate Statement B. For a point to be considered a midpoint, it must meet the condition of dividing the segment into two congruent segments. Therefore, if a point does not divide the segment into two congruent segments, it cannot be a midpoint. Hence, if this condition is satisfied, we can say that Statement B is true.
Since both Statement A and Statement B are true, we can conclude that the given statement is reversible.
The true biconditional statement (if and only if) for this reversible statement is: "A point is a midpoint of a segment if and only if it divides the segment into two congruent segments."