Question

In a A ABC, D and E are points on the sides AB and AC respectively for each of the following
cases, show that DE || BC.
(1) AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm, EC = 5.5 cm​

Answer 1

Here, using the corollary of basic proportionality theorem which states that if a line passing through the two sides of the triangle cuts it proportionally, then the line is parallel to the third side. So

AD=9.55.7=53

ECAE=5.53.3=53

∴  BDAD=ECAE

Thus, as DE cuts the sides AB and AC proportionally, so 

DE II BC.

∴   DE II BC

THNX❣