Question

ln a ∆ABC , D and E are points on the sides AB and AC respectively such that AD =5.7cm , BD =9.5cm , AE =3.3cm and AC =8.8cm ls DE ||BC ?justify your answer.​

Answer 1

Answer:

Converse of basic proportionality theorem :  

If a line divides any two sides of a triangle in the same ratio then the line must be parallel to the third side.

SOLUTION :

Given, :

D and E are the points on sides AB and AC. AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm, and EC = 5.5 cm.

To prove : DE || BC.

In ∆ABC,

AD / DB = 5.7/9.5 = 3/5  

And,  AE/EC = 3.3/5.5 = 3/5

so, AD / DB = AE/EC

Hence, DE || BC.

[By Converse of basic proportionality theorem]

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