Question

identify the theorem you can use to show that the quadrilateral is a parallelogram. parallelogram diagonals converse parallelogram opposite angles converse parallelogram opposite sides converse opposite sides parallel and congruent theorem

Explanation:

The diagram shows the diagonals of the quadrilateral bisecting each other (the segments of the diagonals are 4 and 6, with the intersection creating equal - length segments for each part of the diagonals). The "Parallelogram Diagonals Converse" theorem states that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. The other options: "Parallelogram Opposite Angles Converse" is about opposite angles, "Parallelogram Opposite Sides Converse" is about opposite sides, and "Opposite Sides Parallel and Congruent Theorem" is about sides being both parallel and congruent, which is not indicated by the diagonal lengths here.

Answer:

A. Parallelogram Diagonals Converse