Question

two line segments AC and BD bisect each other at O prove that ABCD is a parallelogram

Answer 1

solution⤵️

Given,
two line segments AC and BD bisect each other at O
=>OA=OC and OB=OD

To prove: ABCD is a parallelogram

construction:AB,BC,CD and DA are joined

proof: in ∆AOB and ∆COD
OA=OC (given)
OB=OD (given)
<AOB=<COD (Vertically opposite angles)
therefore,∆AOB=~∆COD (SAS)
=> <OAB=<COD (CPCT)
=> AB||CD➡️[1]
also AB=CD➡️[2]

from[1] & [2],
ABCD is a parallelogram

hence proved

Answer 2

Answer:

To Prove= ABCD is a parallelogram

PROOF =in traingle AOB and COD

AO=CO

BO=DO

Angle AOB=Angle COD

so proof it is congurent

so angle 1=angle =2 hence parallel it is a quadrilateral and a parallelogram