Question

select the correct answer.
\overline{ac} and \overline{bd} are diagonals of quadrilateral abcd. is quadrilateral abcd a parallelogram? explain.
a. no, because the sides are congruent.
b. yes, because the diagonals bisect each other.
c. no, because the diagonals bisect each other.
d. yes, because the sides are congruent.

Explanation:

Step1: Recall Parallelogram Diagonal Property

A parallelogram has diagonals that bisect each other, meaning \( AO = OC \) and \( BO = OD \).

Step2: Analyze Given Diagram

From the diagram, \( AO = 4 \), \( OC = 4 \) (so \( AO = OC \)) and \( BO = 6 \), \( OD = 6 \) (so \( BO = OD \)). Thus, diagonals bisect each other.

Step3: Evaluate Options

• Option A: Incorrect, diagonals do bisect each other.
• Option B: Correct, as diagonals bisect each other (defining property of parallelogram).
• Option C: Incorrect, diagonals do bisect each other, so answer should be yes.
• Option D: Incorrect, congruent sides aren't the reason here; bisecting diagonals is.

Answer:

B. Yes, because the diagonals bisect each other.