if D and e are respectively the points on the sides ab and ac of a triangle ABC such that ad is equal to 6 cm and BD is equal to 9 cm and a is equals to 8 cm is equal to 12 CM then show that De is parallel to BC
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Given,
AE = 6 CM
EC = 9 CM
AD = 8 CM
DB = 12 CM
Clearly,
AD/DB = 8/12 = 2/3
and,
AE/ EC = 6/9 = 2/3
Hence,
AE/EC = AD/BD
We know that, if a line intersects two sides of triangle in same ratio of sides, Then the intersecting line will be half of third side of triangle and parallel to third side.
Hence,
DE || BD
And,
DE = 1/2 * BC
BC = 2DE
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