which property justifies: if line lm is congruent to line op then line op is congruent to line lm?
commutative
The property that justifies the statement "if line LM is congruent to line OP, then line OP is congruent to line LM" is the Symmetric Property of Congruence.
To understand this property, let's first define congruence. Two line segments are said to be congruent if they have the same length. In other words, if you can place one line segment directly on top of the other so that they perfectly overlap, then they are congruent.
The Symmetric Property of Congruence states that if two things are congruent, then you can reverse their order and still have a true statement.
In the given statement, it is stated that line LM is congruent to line OP. So, according to the Symmetric Property of Congruence, it can be concluded that line OP is congruent to line LM as well. This means that the order in which the line segments are mentioned does not affect their congruence.
To summarize, the Symmetric Property of Congruence justifies that if line LM is congruent to line OP, then line OP is congruent to line LM.