Question

question 2 of 10
if the diagonals of a quadrilateral bisect each other, it is a parallelogram.
a. true
b. false

Explanation:

Step1: Recall parallelogram property

One of the key properties of a parallelogram is that its diagonals bisect each other. Also, 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 \(BO=OD\), then \(\triangle AOB\cong\triangle COD\) (by the Side - Angle - Side (SAS) congruence criterion since \(\angle AOB=\angle COD\) (vertically opposite angles), \(AO = OC\) and \(BO = OD\)). From the congruence of these triangles, we can show that opposite sides are parallel, which is the definition of a parallelogram.

Answer:

A. True