Prove the indicated result of Proposition 35 in question #8 that pertains from Book 1 of Euclid’s Elements.
Consider the given figure:
Now, in triangle ABC and DCF :
AB=CD (since, ABCD is a parallelogram)
∠ABE = ∠DCF (since, ∠BAD= ∠CDF and Angle ∠AEB = angle ∠DFC)
BE=CF (since, BEFC is a parallelogram)
Thus, by SAS property:
∆ABC ≡ ∆DCF
Ar (∆ABC) = Ar (∆DCF)
Ar (ABGD)+ Ar (DGE) = Ar (EFCG) + Ar (DGE)
Ar (ABGD) = Ar (EFCG)
Now, add the area of triangle BGC to both sides:
Ar (ABGD)+ Ar (BGC) = Ar (EFCG) + Ar (BGC)
Ar (ABCD) = Ar (BCF...
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