Question

question 2 of 27 which of the following is a valid reason why the quadrilateral shown below is a parallelogram? a. the diagonals bisect each other. b. both pairs of opposite sides are parallel. c. the diagonals are congruent. d. both pairs of opposite sides are congruent.

Explanation:

To determine why the quadrilateral is a parallelogram, we analyze the diagram and the options:

• Option A: The diagram shows the diagonals intersecting at \( W \) with markings indicating \( IW = WK \) and \( HW = WJ \), meaning the diagonals bisect each other. A theorem states that if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.
• Option B: The diagram does not show markings or information about opposite sides being parallel.
• Option C: The diagram does not indicate the diagonals are congruent (equal in length), and congruent diagonals alone do not prove a quadrilateral is a parallelogram (e.g., isosceles trapezoid has congruent diagonals but is not a parallelogram in general).
• Option D: The diagram does not show markings for opposite sides being congruent.

So the valid reason is that the diagonals bisect each other.

Answer:

A. The diagonals bisect each other.