How can prove that diagonal are not equal of a parallelogram.
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the diagonal of parallelogram are not equal because when the only opposite sides of parallelogram are equal
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Given - We have a parallelogram ABCD
To prove -We need to prove that diagonals of a parallelogram bisect each other
Proof - We join A & C i.e. we draw diagonal AC. We join B & D i.e. we draw diagonal BD . Say AC and BD intersect point at o
In Δ AOD & ΔBOC
∠BOC=∠AOD ( Vertically opposite angles are equal )
∠BCO=∠OAD ( Alternate interior angles are equal )
AD = BC ( opposite sides of ║gm are equal)
∴ ΔAOD ≅ ΔBOC by A.A.S.
By C.P.C.T. - OB=OD & OC=OA
Hence proved
To prove -We need to prove that diagonals of a parallelogram bisect each other
Proof - We join A & C i.e. we draw diagonal AC. We join B & D i.e. we draw diagonal BD . Say AC and BD intersect point at o
In Δ AOD & ΔBOC
∠BOC=∠AOD ( Vertically opposite angles are equal )
∠BCO=∠OAD ( Alternate interior angles are equal )
AD = BC ( opposite sides of ║gm are equal)
∴ ΔAOD ≅ ΔBOC by A.A.S.
By C.P.C.T. - OB=OD & OC=OA
Hence proved
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