Question

AB and CD intersect each other at O and O is the mid-point of both AB and CD. Prove that AC = BD and AC || BD.

Answer 1

Following are the proving to this question:

Explanation:

Please find the graph image in the attachment.

Given O is the mid-point of AB and CD

`\to OA=OB \\\\\to OC=OD\\\\In\ \Delta AOD,\Delta BOC\\\\AO=BO\\\\ CO=DO\\\\ \angle AOD= \angle BOC (\text{vertically opposite angles}) \\\\`

`By \ S.A.S \ congruency \\\\\Delta AOD \cong \Delta BOC \\\\\to AD=BC`