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Diagonal ac and bd of a …

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Diagonal ac and bd of a trapezium abcd with ab parallel to dc intersect each other at point o .show that oa/oc=ob/od

Posted by Swayam Mishra 6 years, 3 months ago

CBSE > Class 10 > Mathematics

2 answers

Gaurav Seth 6 years, 3 months ago

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

0Thank You

Kishan Dattarwal 6 years, 3 months ago

Use bpt

1Thank You

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CBSE > Class 10 > Mathematics