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Question
In ΔABC, D and E are points on the sides AB and AC respectively. For the following case show that DE || BC
AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm.
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Solution
Here AB = 5.6 cm, AD = 1.4 cm, BD = AB – AD
= 5.6 – 1.4
= 4.2
AC = 7.2 cm, AE = 1.8 cm, EC = AC – AE
= 7.2 – 1.8
EC = 5.4 cm
`"AD"/"DB" = 1.4/4.2 = 1/3`
`"AE"/"EC" = 1.8/5.4 = 1/3`
`"AE"/"EC" = "AD"/"DE"`
By converse of basic proportionality theorem DE || BC
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