Question

if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
a. true
b. false

Explanation:

Step1: Recall geometric property

One of the well - known properties in geometry is that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. This can be proven using congruent triangles. Let the quadrilateral be \(ABCD\) with diagonals \(AC\) and \(BD\) intersecting at point \(O\). If \(AO = OC\) and \(BO=OD\), we can show that \(\triangle AOB\cong\triangle COD\) and \(\triangle AOD\cong\triangle COB\) by the Side - Angle - Side (SAS) congruence criterion. From the congruence of these triangles, we can get equal opposite sides and parallel opposite sides, which are the characteristics of a parallelogram.

Answer:

A. True