Start with writing the statement as a conditional statement.
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.
Practice makes perfect
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.
