As shown in the figure, it is known that in the quadrilateral ABCD, points E and F are on AD and BC respectively, and EF bisects the diagonal AC perpendicularly, and the vertical foot is O. Let’s talk

As shown in the figure, it is known that in the quadrilateral ABCD, points E and F are on AD and BC respectively, and EF bisects the diagonal AC perpendicularly, and the vertical foot is O. Let’s talk about the quadrilateral.

Because EF bisects AC perpendicularly, AF=AE, CF=CE, angle AOE=angle COF=90 degrees

In parallelogram ABCD, AO=CO, AD is parallel to BC, that is, AC is parallel to EF

So angle EAC = angle FCA

In triangle AOE and triangle COF

Angle AOE = angle COF

Angle EAC = angle FCA

AO=CO

So triangle AOE is equal to triangle COF (AAS)

So AE=CF

So AF=AE=CF=CE

So AFCE is a rhombus