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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
AB = 2cm, AD = 8cm, AE = 12 cm and AC = l8cm.
Solution
AB = 12 cm, AD = 12 cm and AC = 18 cm.
∴ DB = AB – AD
= 12 – 8
⇒ DB = 4 cm
And, EC = AC – AE
= 18 – 12
⇒ EC = 6 cm
Now, `"AD"/"DB"=8/4=2/1` [∵ DB = 4 cm]
And, `"AE"/"EC"=12/6=2/1` [∵ EC = 6 cm]
`rArr"AD"/"DB"="AE"/"EC"`
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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