Question

from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: quadrilateral lpqv, ∠plv ≅ ∠pqv, ∠lpq ≅ ∠qvl prove: lpqv is a parallelogram.

Explanation:

A quadrilateral is a parallelogram if both pairs of opposite angles are congruent. In quadrilateral \(LPQV\), we are given that \(\angle PLV\cong\angle PQV\) and \(\angle LPQ\cong\angle QVL\). These are the two pairs of opposite angles of the quadrilateral \(LPQV\).

Answer:

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