We have been given the following statement.

A perpendicular bisector of a segment is line, segment, or ray that is perpendicular to a segment at its midpoint.

In order to test if the statement is reversible, we will write it as a conditional statement.

If p, then q .

Let's do it!

If a line, segment, or ray is a perpendicular bisector of a segment, then it is perpendicular to a segment at its midpoint.

Next, we will write the converse of the conditional statement as the following.

If q, then p .

If the converse of the statement is true, we can combine two conditional statements as a biconditional statement.

If a line, segment, or ray is perpendicular to a segment at its midpoint, then it is a perpendicular bisector of a segment.

Depending on the definition of a perpendicular bisector, we can say that the statement is reversible. Thus, we can combine the conditional statements as a biconditional.

p if and only if q .

Let's combine them!

A line, segment, or ray is a perpendicular bisector of a segment if and only if it is perpendicular to a segment at its midpoint.

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