name the property of equality that justifies the statement if lm=op then op=lm
The property of equality that justifies the statement "if lm = op, then op = lm" is the symmetric property of equality. According to this property, if a = b, then b = a.
The property of equality that justifies the statement "if LM = OP, then OP = LM" is the symmetric property of equality.
Explanation on how to determine the property:
To verify which property of equality is used in this statement, we need to understand the different properties of equality:
1. Reflexive Property: A quantity is equal to itself. (For example, AB = AB)
2. Symmetric Property: If two quantities are equal, then changing the order does not affect equality. (For example, if AB = CD, then CD = AB)
3. Transitive Property: If two quantities are equal to a third quantity, then they are equal to each other. (For example, if AB = CD and CD = EF, then AB = EF)
In the given statement "if LM = OP, then OP = LM," we see that it involves two quantities, LM and OP. The statement states that if LM is equal to OP, then OP is also equal to LM. This change in the order of the quantities implies the use of the symmetric property of equality.
Therefore, the symmetric property of equality justifies the statement "if LM = OP, then OP = LM."