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Question

Given a parallelogram ABCD. Prove that OC=OA
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Solution

Given:- ABCD is a parallelogram with AC&BD as diagonals.
ABCD is a parallelogram.
ADBCBDA=CBD and DAC=ACB ...... (alternate angles)
orODA=CBO and DAO=OCB........(i)
Now between ΔADO and ΔCOB we have AD=BC ...... (opposite side of a parallelogram)
ODA=CBO and DAO=OCB ..... by (i)
By ASA test ΔAOD and ΔCOB are congruent.
OC=OA

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