Which statement about parallelograms is always true?
A The diagonals are congruent:
B The diagonals bisect each other.
C The diagonals are perpendicular:
D The diagonals bisect their respective angles
The correct answer and explanation is:
The correct answer is B: The diagonals bisect each other.
Explanation:
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. The properties of parallelograms are quite specific, and understanding their diagonals is crucial. Here’s a breakdown of why option B is correct:
- The diagonals bisect each other: This property is always true for any parallelogram. When two diagonals of a parallelogram intersect, they divide each other into two equal parts. This means that the point of intersection of the diagonals is the midpoint of both diagonals. This property holds for all types of parallelograms, including rectangles, rhombuses, squares, and general parallelograms.
Let’s look at the other options:
- A: The diagonals are congruent: This is not always true for all parallelograms. Only special types of parallelograms, such as rectangles and squares, have congruent diagonals. In general parallelograms, the diagonals can be of different lengths.
- C: The diagonals are perpendicular: Again, this property is not true for all parallelograms. It only holds for specific cases, such as rhombuses. In a general parallelogram, the diagonals are not necessarily perpendicular to each other.
- D: The diagonals bisect their respective angles: This property is specific to rhombuses (and squares, which are a special type of rhombus). In general parallelograms, the diagonals do not necessarily bisect the angles at the vertices.
Thus, the diagonals bisecting each other is the only property that holds true for all parallelograms.