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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 = 12 cm, AD = 8 cm, AE = 12 cm and AC = 18 cm
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Solution
Here AB = 12 cm, BD =12 – 8 = 4 cm, AE =12 cm, EC = 18 – 12 = 6 cm
∴ `"AD"/"DB" = 8/4` = 2
`"AE"/"EC" = 12/6` = 2
`"AD"/"DB" = "AE"/"EC"`
By converse of basic proportionality theorem DE || BC
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