Question

In `DeltaABC,D` and E are points on the sides AB and AC respectively. Find whether DE||BC if
(i) AD= 3cm , BD = 4.5cm, AE = 4cm, AC= 10cm
(ii) AB=7 cm , BD = 4.5cm, AE = 3.5 cm, CE= 5.6cm.

Answer 1

DE will be parallel to BC, only when `(AD)/(BD)= (AE)/(CE)`
(i) Since AD=3 cm , BD = 4.5 cm, AE= 4cm and CE= AC-AE = 10 cm -4cm = 6cm
` (AD)/(BD) = 3/(4.5) = 2/3`
and `(AE)/(CE)= 4/6 = 2/3`
`(AD)/(BD)=(AE)/(CE)`
DE||BC
`(AD)/(BD) = (7-4.5)/(4.5) = (2.5)/(4.5) = 5/9`
`(AE)/(CE) = (3.5)/ (5.6) = 5/8`
since `(AD)/(BD) ne (AE)/(CE)`
DE is not parallel to BC.