Q5 of 23 Page 1

Solve sub-questions:

Prove that, if a line parallel to a side of a triangle intersect the other sides in two district points, then the line divides those sides in proportion.

Given: A Δ ABC in which DE||BC, and intersect AB in D and AC in E.


Prove:


Construction: Join BE, CD and draw EF⊥ BA and DG⊥CA.



Proof:


Area ∆ADE ==


Area ∆DBE = =


⇒


Similarly,


⇒


ΔDBE and ΔDEC are on the same base DE and bw the same parallel DE and BC.


∴ Area (Δ DBE) = Area (ΔDEC)


⇒ [Taking reciprocal of both sides]


⇒ [Multiplying both sides by Area (Δ ADE)]


⇒


Hence Proved.


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