Question

Please tell me the answer.

Answer 1

In ∆DEO and ∆BFO
angle DEO=angle BFO(90°each)
angle DOE=angle BOF(vertically opposite angles)
DO = BO(given)
→∆DEO is congrent to ∆BFO. (1)

Similarly,
In ∆DEC and ∆BFA
angle DEC=angle BFA(90°each)
DC=BA(given)
DE=BF(cpct)
→∆DEC is congrent to ∆BFA. (2)

Adding (1) and (2)
→∆DOC is congrent to ∆ BOA
→ar(DOC)=ar(BOA)
(i) is now proved


We know that,
ar(DOC)=ar(BOA)
→ ar(DOC) + ar(COB)=ar(BOA) + ar(COB)
→ ar(DCB)=ar(ACB)

(ii) is now proved


We know that,
ar(DCB)=ar(ACB)
But,
they lie on the same base that is CB
and also have same area
→DA||CB
(iii) is now proved.


Hope this helps you.Thank you.