Final answer:
The segment connecting the midpoints of opposite sides in a quadrilateral bisect each other.
Step-by-step explanation:
The segment connecting the midpoints of opposite sides in a quadrilateral bisect each other.
To prove this, let ABCD be the quadrilateral with midpoints M and N on AB and CD, respectively. We need to show that the segment MN bisects both AC and BD.
Using the midpoint theorem, we know that AM = MB and CN = ND. Therefore, we can conclude that MN bisects both AC and BD.