Question

from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: parallelogram lpqv prove: \\( \overline { p m } \cong \overline { m v } \\), \\( \overline { l m } \cong \overline { m q } \\)

Explanation:

Step1: Recall the property of parallelogram

In a parallelogram, the diagonals bisect each other.

Step2: Apply the property to the given parallelogram

Since \(LPQV\) is a parallelogram and \(PV\) and \(LQ\) are its diagonals intersecting at \(M\). By the property of parallelogram (diagonals bisect each other), we have \(PM = MV\) (so \(\overline{PM}\cong\overline{MV}\)) and \(LM=MQ\) (so \(\overline{LM}\cong\overline{MQ}\))

Answer:

The property (diagonals of a parallelogram bisect each other) justifies the prove statement.