If D and E are respectively the points on the side AB and AC of a triangle ABC such that AD = 6 cm, BD = 9 cm, AE = 8 cm and EC = 12 cm, then show that DE || BC.
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Answered by
3
Answer:
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
Answered by
7
First prove the converse of BPT theorem to show that the ratio between the sides of two triangles are equal.
AD/BD=AE/EC
6/9=8/12
2/3=2/3
Therefore by converse of BPT,
DE || BC
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