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. 

AB = 10.8 cm, AD = 6.3 cm, AC = 9.6 cm and EC = 4 cm.

 

Answer 1

We have:
AB = 10.8 cm, AD = 6.3 cm
Therefore, 

 DB = 10.8 – 6.3 = 4.5 cm
Similarly,
AC = 9.6 cm, EC = 4cm
Therefore,
AE = 9.6 – 4 = 5.6 cm
Now,
`(AD)/(DB)=6.3/4.5=7/5`

`(AE)/(EC)=5.6/4=7/5`   

⟹`(AD)/(DB)=(AE)/(EC)`
Applying the converse of Thales’ theorem,
We conclude that DE ‖ BC.