Which statement about parallelogram diagonals is true?

Which statement about parallelogram diagonals is true?

• A. Diagonals bisect each other
• B. Diagonals are perpendicular
• C. Diagonals are equal in length
• D. Diagonals do not intersect

Answer: (A)

In a parallelogram, diagonals bisect each other. When the two diagonals cross, the parallel opposite sides create pairs of congruent triangles around the intersection. Those congruent triangles force the point where the diagonals cross to be the midpoint of each diagonal, so each diagonal is split into two equal halves at the intersection. That means the diagonals are not necessarily perpendicular, nor are they necessarily equal in length. They do intersect, which is also true, but the defining property here is that the intersection point divides both diagonals into equal segments.

In a parallelogram, diagonals bisect each other. When the two diagonals cross, the parallel opposite sides create pairs of congruent triangles around the intersection. Those congruent triangles force the point where the diagonals cross to be the midpoint of each diagonal, so each diagonal is split into two equal halves at the intersection.

That means the diagonals are not necessarily perpendicular, nor are they necessarily equal in length. They do intersect, which is also true, but the defining property here is that the intersection point divides both diagonals into equal segments.