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Question
In ΔABC, D and E are the points on sides AB and AC respectively. Find whether DE || BC, if:
- AB = 9 cm, AD = 4 cm, AE = 6 cm and EC = 7.5 cm.
- AB = 6.3 cm, EC = 11.0 cm, AD = 0.8 cm and AE = 1.6 cm.
Solution
i. In ΔADE and ΔABC,
`(AE)/(EC) = 6/7.5 = 4/5`
`(AD)/(BD) = 4/5` ...(Since AB = 9 cm and AD = 4 cm)
So, `(AE)/(EC) = (AD)/(BD)`
∴ DE || BC ...(By the converse of mid-point theorem)
ii. In ΔADE and ΔABC,
`(AE)/(EC) = 1.6/11 = 0.8/5.5`
`(AD)/(BD) = (0.8)/(6.3 - 8) = 0.8/5.5`
So, `(AE)/(EC) = (AD)/(BD)`
∴ DE || BC ...(By the converse of mid-point theorem)
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