In the given figure AB is trisected at D and F and DE||GF||BC if BC=6 cm , then FG equals
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Answer:
TO PROVE : AF : FC = ?
CONSTRUCTION: DG // BF
PROOF : In triangle ADG,
AE = ED ( given)
EF // DG ( by construction)
So AF = FG……. ………(1) (a line passing through the mid point of any side of a triangle, parallel to the other side, bisects the third side)
Now in triangle CBF
BD = DC ( given)
DG // BF ( by construction)
So, FG = GC ( Same reason) ……..(2)
Now, by (1) & (2)
AF = FG = GC
=> AF : FC = 1:2
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