Question

D and E are points on the sides AB and AC respectively of a ∆ABC. If AB = 10.8 cm, AD = 6.3 cm, AC = 9.6 cm and EC = 4 cm. Determine whether DE || BC or not.

Answer 1

From figure, D and E are the points on the sides AB and AC of ∆ABC.

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

DB = AB – AD = 10.8 – 6.3 = 4.5 cm

AE =AC – EC = 9.6 – 4 = 5.6 cm

AD /DB = 6.3/4.5 = 7/5

AE/EC = 5.6/4 = 7/5

=> AD/DB = AE/EC

=> DE || BC