Q18 of 109 Page 300

In the adjoining figures, is a parallelogram in which is produced to so that Prove that bisects

ABCD is parallelogram.


In ∆ODC and ∆​OEB, we have,
DC = BE …as DC = AB
∠COD = ∠BOE … Vertically opposite angles are equal
∠OCD = ∠OBE … Alternate angles with transversal BC
Hence, by SAA test for congruency, we get,
∆​ODC ≅ ∆​OEB


∴ OC = OB …by cpct
We know that BC = OC + OB.
∴ ED bisects BC.


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