Question

which of the following is true about the diagonals of a parallelogram? select the best answer from the choices provided. a. they are congruent. b. they are perpendicular to each other. c. they bisect each other. d. they bisect the opposite angles.

Explanation:

• Option A: Diagonals of a parallelogram are congruent only in special cases like rectangles (a type of parallelogram). But it is not a general property of all parallelograms.
• Option B: Diagonals are perpendicular to each other in special parallelograms like rhombuses. It is not a property of all parallelograms.
• Option C: By the property of parallelograms, the diagonals bisect each other. In parallelogram \(ABCD\) with diagonals \(AC\) and \(BD\) intersecting at point \(O\), \(\triangle AOB\cong\triangle COD\) (by \(ASA\) criterion since \(AB\parallel CD\), \(AB = CD\), \(\angle BAO=\angle DCO\) and \(\angle ABO=\angle CDO\)), so \(AO = OC\) and \(BO=OD\).
• Option D: Diagonals bisect the opposite angles in rhombuses (a type of parallelogram). It is not a property of all parallelograms.

Answer:

C. They bisect each other.