Question
In the given figure, AB | | DC. Show that ar(BDE) = ar(ACED).
Solution
Given: AB || DC in the given figure.
To Prove: ar(BDE) = ar(ACED)
Proof: ∵ ΔADC and ΔBDC are on the same base DC and between the same parallels AB and DC ∴ ar(ΔADC) = ar(ΔBDC)
⇒ ar(ΔADC) + ar(ΔDCE)
= ar(ΔBDC) + ar(ΔDCE)
| Adding ar(ΔDCE) to both sides ⇒ ar(ACED) = ar(BDE)
⇒ ar(BDE) = ar(ACED)
