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Question
D and E are points on the sides AB and AC respectively of a ΔABC. In each of the following cases, determine whether DE║BC or not.
AD = 7.2cm, AE = 6.4cm, AB = 12cm and AC = 10cm.
Solution
We have :
AD = 7.2 cm, AB = 12 cm
Therefore,
DB = 12 – 7.2 = 4.8 cm
Similarly,
AE = 6.4 cm, AC = 10 cm
Therefore,
EC = 10 – 6.4 = 3.6 cm
Now,
`(AD)/(DB)=7.2/4.8=3/2`
`(AE)/(EC)=6.4/3.6=16/9`
This,` (AD)/(DB)≠(AE)/(EC)`
Applying the converse of Thales’ theorem,
We conclude that DE is not parallel to BC.
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