Question

D and E are points on the sides AB and AC respectively of Δ ABC such that AB=5.6cm, AD= 1.4cm, AC=7 .2cm and AE = 1.5 cm, show that DE is parallel to BC

Answer 1

To prove : DE || BC

Sol : AB = 5.6 cm  AC = 7.2 cm

AD = 1.4 cm   AE = 1.8 cm

DB = 4.2 cm    EC = 5.4 cm

`"AD"/"DB" = 1.4/4.2 = 1/3`    ...(1)

`"AE"/"EC" = 1.8/5.4 = 1/3`  ....(2)

From (1) and (2)

`"AD"/"DB" = "AE"/"EC"`

∴ DE || BC (by concerse of BPT)