In the adjoining figure, DE || BC. Prove that

Question:

In the adjoining figure, DE || BC. Prove that
(i) ar(ACD) = ar(ABE),
(ii) ar(OCE) = ar(OBD),

 

Solution:

DEC and ​∆DEB lies on the same base and between the same parallel lines.
So, ar(​∆DEC) = ar(∆DEB)                      ...(1)

(i) On adding​ ar(∆ADE)​ in both sides of equation (1), we get:
ar(​∆DEC) + ar(∆ADE)​ = ar(∆DEB) + ar(∆ADE)​ ​                 
⇒ ar(​​∆ACD) = ar(​​∆ABE

(ii) On subtracting​ ar(ODE)​ from both sides of equation (1), we get:​
ar(​∆DEC-">- ar(∆ODE)​ = ar(∆DEB-">- ar(∆ODE)​ ​      ​
⇒ ar(​​∆OCE) = ar(​∆OBD)

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