Question

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

Explanation:

Step1: Recall the definition of a parallelogram

A parallelogram is a quadrilateral with both pairs of opposite sides parallel. However, there is also a theorem that states: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Step2: Apply the theorem to the given problem

We are given that in quadrilateral \(ABCD\), \(\overline{AB}\cong\overline{CD}\) and \(\overline{AD}\cong\overline{BC}\). This matches the condition of the theorem "If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram".

Answer:

The theorem "If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram" justifies the statement that \(ABCD\) is a parallelogram.