Geometry CBE Practice Exam

In a parallelogram, the diagonals bisect each other. If you label the parallelogram ABCD with diagonals AC and BD intersecting at E, the opposite sides are parallel in pairs, AB ∥ CD and BC ∥ AD. This parallelism creates congruent triangles around the intersection, which forces AE = EC and BE = ED. So the intersection point E splits each diagonal into two equal segments, meaning the diagonals cut each other in half.

The other statements aren’t guaranteed for every parallelogram: diagonals aren’t necessarily perpendicular (that happens in special cases like a rhombus or square), they aren’t necessarily equal in length (only in special cases like a rectangle), and they do intersect (so saying they do not intersect is false).