Question

D and E are points on the sides AB and AC respectively of a ΔABC. In the following cases, determine whether DE || BC or not. 

AD = 7.2 cm, AE = 6.4 cm, AB = 12 cm and AC = 10 cm.  

 

Answer 1

We have :
AD = 7.2 cm, AB = 12 cm
Therefore,
DB = 12 – 7.2 = 4.8 cm
Similarly,
AE = 6.4 cm, AC = 10 cm
Therefore,
EC = 10 – 6.4 = 3.6 cm
Now,
`(AD)/(DB)=7.2/4.8=3/2`
`(AE)/(EC)=6.4/3.6=16/9`
This,` (AD)/(DB)≠(AE)/(EC)`
Applying the converse of Thales’ theorem,
We conclude that DE is not parallel to BC.