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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.
AB = 10.8cm, AD = 6.3cm, AC = 9.6cm and EC = 4cm.
Solution
We have:
AB = 10.8 cm, AD = 6.3 cm
Therefore,
DB = 10.8 – 6.3 = 4.5 cm
Similarly,
AC = 9.6 cm, EC = 4cm
Therefore,
AE = 9.6 – 4 = 5.6 cm
Now,
`(AD)/(DB)=6.3/4.5=7/5`
`(AE)/(EC)=5.6/4=7/5`
⟹`(AD)/(DB)=(AE)/(EC)`
Applying the converse of Thales’ theorem,
We conclude that DE ‖ BC.
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