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Question
In fig. ABCD is a trapezium in which AB | | DC and AB = 2DC. Determine the ratio between the areas of ΔAOB and ΔCOD.
Solution
In triangle AOB and COD, we have
∠AOB = ∠COD, ...[Vertically opposite angles]
and ∠OAB = ∠OCD, ...[Corresponding angles]
So, by AA-criterion of similarly, we have
ΔAOB ∼ ΔCOD
⇒ `"Area (ΔAOB)"/"Area (ΔCOD)" = "AB"^2/"DC"^2`
⇒ `"Area (ΔAOB)"/"Area (ΔCOD)" = (2"DC")^2/("DC")^2`
= `(4)/(1)`
Hence, area (ΔAOB) : area(ΔCOD) = 4 : 1.
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