Question

from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: \\( \overline { a e } \cong \overline { i o } \\), \\( \overline { a o } \cong \overline { e i } \\) prove: aeio is a parallelogram.

Explanation:

Step1: Recall the parallelogram theorem

One of the theorems for parallelograms states that 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

In quadrilateral \(AEIO\), we are given that \(\overline{AE}\cong\overline{IO}\) (one pair of opposite sides) and \(\overline{AO}\cong\overline{EI}\) (the other pair of opposite sides).

Answer:

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