Question

from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: quadrilateral rstu; \\( \overline { s p } \cong \overline { u p } \\) and \\( \overline { r p } \cong \overline { p t } \\) prove: rstu is a parallelogram.

Explanation:

Step1: Recall parallelogram theorems

One of the theorems for parallelograms states that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Step2: Analyze given information

We are given that \(\overline{SP}\cong\overline{UP}\) (so \(P\) is the mid - point of \(SU\)) and \(\overline{RP}\cong\overline{PT}\) (so \(P\) is the mid - point of \(RT\)). This means the diagonals \(SU\) and \(RT\) of quadrilateral \(RSTU\) bisect each other at point \(P\).

Answer:

The theorem that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram justifies that \(RSTU\) is a parallelogram.