Question

problem 16:
(first taught in
lesson 55)
from this given statement,
select the definition, property,
postulate, or theorem that jus-
tifies each prove statement. i
given: quadrilateral ijkl, \\( \overline { i j } \parallel \overline { l k } \\), \\( \overline { i j } \cong \overline { l k } \\)
prove: ijkl is a parallelogram.

Explanation:

Step1: Recall parallelogram definition

A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Also, there is a theorem: If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.

Step2: Apply the theorem

In quadrilateral \(IJKL\), we are given that \(\overline{IJ}\parallel\overline{LK}\) (parallel) and \(\overline{IJ}\cong\overline{LK}\) (congruent). This satisfies the condition of the theorem.

Answer:

The theorem that if one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.