Question

In Δ , D and E are points on the sides AB and AC respectively. Show that DE ∥ BC if AB = 10.8cm, BD = 4.5cm, AC = 4.8cm and AE = 2.8cm

Answer 1

Given : D and E are the points on sides AB and AC.   AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm, and AE = 2.8 cm

To prove : DE || BC.

AD = AB – DB  

AD = 10.8 – 4.5

AD = 6.3 cm

EC = AC – AE  

EC = 4.8  – 2.8  

EC = 2 cm

In ∆ABC,

AD / DB = 6.3/4.5 = 7/5  = 1.4

And,  AE/EC = 2.8 /2.0 = 1.4

so, AD / DB = AE/EC

Hence, DE || BC.

[By Converse of basic proportionality theorem]