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Question
In a ΔABC, D and E are points on the sides AB and AC respectively. For the following case show that DE || BC
AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm.
Solution
We have,
DE || BC
We have, AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm
Now, `"AD"/"DB"=5.7/9.5=57/95`
`rArr"AD"/"DB"=3/5`
And, `"AE"/"EC"=3.3/5.5=33/55`
`rArr"AE"/"EC"=3/5`
Thus DE divides sides AB and AC of ΔABC in the same ratio.
Therefore, by the converse of basic proportionality theorem.
We have DE || BC
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