Math, asked by LibinD, 1 year ago

Diagonals AC and BD of a trapezium ABCD with AB\\DC intersect each other at the point O.Using a simiarity criterion for two triangles Show that OA/OC=OB/OD

Answers

Answered by smartcow1
96
Hey there,

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 this helps!

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LibinD: After the proves of AAA theorem any other steps to follow
Answered by priyankarout1979
18

Answer:

Step-by-step explanation:

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