Question

from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: quadrilateral abcd, ( overline{ab} cong overline{cd} ), ( overline{ad} cong overline{bc} ) prove: abcd is a parallelogram.

Explanation:

A parallelogram is defined as a quadrilateral with both pairs of opposite sides parallel. However, one of the theorems for proving a quadrilateral is a parallelogram states that if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. In this case, since \(\overline{AB}\cong\overline{CD}\) and \(\overline{AD}\cong\overline{BC}\), this theorem applies.

Answer:

The theorem that if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.