teFazoe7213 teFazoe7213
  • 23-03-2021
  • Mathematics
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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.

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codiepienagoya codiepienagoya
  • 25-03-2021

Answer:

Following are the proving to this question:

Step-by-step explanation:

Please find the graph image in the attachment.

Given O is the mid-point of AB and CD

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

[tex]By \ S.A.S \ congruency \\\\\Delta AOD \cong \Delta BOC \\\\\to AD=BC[/tex]

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