Question

using the given information below, which test for parallelograms proves that defg is a parallelogram? image of quadrilateral defg with e, f, g, d labeled and two sides (de and fg) marked congruent options: opposite sides are parallel; opposite sides are congruent; one pair of opposite sides is parallel and congruent; opposite angles are congruent

Explanation:

To determine the test for parallelograms, we analyze the diagram. The marks on sides \( DE \) and \( FG \) indicate they are congruent (equal in length). The test "Opposite sides are congruent" states that if both pairs of opposite sides of a quadrilateral are congruent, it is a parallelogram. Here, the markings show one pair ( \( DE \) and \( FG \)) is congruent, and by the property, if opposite sides are congruent, the quadrilateral is a parallelogram. The other options: "Opposite sides are parallel" would require parallel markings (like arrows), "One pair of opposite sides is parallel and congruent" needs both parallel and congruent markings for one pair, and "Opposite angles are congruent" isn't indicated here. So the correct test is "Opposite sides are congruent".

Answer:

Opposite sides are congruent