Question

Abcd is a trapezium in which ab cd and diagonals ac and bd intersect at o using a similarity criterian . Prove that oa/oc=ob/od

Answer 1

Answer:

In ΔDOC and ΔBOA,

∠CDO = ∠ABO [Alternate interior angles as AB || CD]

∠DCO = ∠BAO [Alternate interior angles as AB || CD]

∠DOC = ∠BOA [Vertically opposite angles]

∴ ΔDOC ~ ΔBOA [AAA similarity criterion]

∴ DO/BO = OC/OA  [ Corresponding sides are proportional]

⇒ OA/OC = OB/OD .

Hope it will help you...❤

Answer 2

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