Question

7. In the given figure, AB|| DC. Show that
ar (ABDE) = ar (A ACED).​

Answer 1

Step-by-step explanation:

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(ABDE)

⇒ ar(ABDE) = ar(ACED)