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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 = 5.6cm, AD = 1.4cm, AC= 7.2 cm and AE = 1.8 cm.
Solution
We have,
AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm
∴ DB = AB – AD
= 5.6 – 1.4
⇒ DB = 4.2 cm
And, EC = AC – AE
= 7.2 – 1.8
⇒ EC = 5.4 cm
Now, `"AD"/"DB"=1.4/4.2=1/3` [∵ DB = 4.2 cm]
And, `"AE"/"EC"=1.8/5.4=1/3` [∵ EC = 5.4 cm]
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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