Question

(c) problem 16: (first taught in lesson 54) from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: quadrilateral lpqv, \\( \overline { p l } \cong \overline { q v } \\), \\( \overline { l v } \cong \overline { p q } \\) prove: lpqv is a parallelogram.

Explanation:

Step1: Recall parallelogram theorems

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: Identify opposite sides

In quadrilateral \(LPQV\), \(\overline{PL}\) and \(\overline{QV}\) are one pair of opposite sides, and \(\overline{LV}\) and \(\overline{PQ}\) are the other pair of opposite sides.

Step3: Apply the theorem

Since \(\overline{PL}\cong\overline{QV}\) and \(\overline{LV}\cong\overline{PQ}\) (given), by the theorem that if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Answer:

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