Question

In ΔABC, D and E are the points on sides AB and AC respectively. Find whether DE || BC, if:

1. AB = 9 cm, AD = 4 cm, AE = 6 cm and EC = 7.5 cm.
2. AB = 6.3 cm, EC = 11.0 cm, AD = 0.8 cm and AE = 1.6 cm.

Answer 1

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)