Question

practice c: (first taught in lesson 53) from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: parallelogram abcd prove: \\( \overline { ap } \cong \overline { pc } \\) and \\( \overline { bp } \cong \overline { pd } \\)

Explanation:

Step1: Recall parallelogram properties

In a parallelogram, the diagonals bisect each other.

Step2: Apply property to given parallelogram

For parallelogram \(ABCD\) with diagonals \(AC\) and \(BD\) intersecting at \(P\), by the property of parallelogram diagonals bisecting each other, we have \(AP = PC\) (so \(\overline{AP}\cong\overline{PC}\)) and \(BP = PD\) (so \(\overline{BP}\cong\overline{PD}\)).

Answer:

The property of a parallelogram that the diagonals bisect each other justifies the statement \(\overline{AP}\cong\overline{PC}\) and \(\overline{BP}\cong\overline{PD}\).