Question

from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: quadrilateral rstu;
overline{rs} parallel overline{ut} and overline{rs} cong overline{ut} prove: rstu is a parallelogram.

Explanation:

A parallelogram is defined as a quadrilateral with both pairs of opposite sides parallel. However, there is also a theorem that states if one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram. In this case, we are given that \( \overline{RS}\parallel\overline{UT}\) and \( \overline{RS}\cong\overline{UT}\). This matches the conditions of the theorem.

Answer:

The theorem that if one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.