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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 = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm.
Solution
We have,
AB = 10.8cm, BD = 4.5cm, AC = 4.8 cm and AE = 2.8cm
∴ AD = AB – DB = 10.8 – 4.5
⇒ AD = 6.3 cm
And, EC = AC – AE
= 4.8 – 2.8
⇒ EC = 2 cm
Now, `"AD"/"DB"=6.3/4.5=7/5` [∵ AD = 6.3 cm]
And, `"AE"/"EC"=2.8/2=28/20=7/5` [∵ EC = 2 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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