Question

In a given ∆ ABC , D and E are points on the sides AB and AC respectively. If AB = 12cm , AD = 8cm AE = 12cm and AC= 18 cm. Is DE || BC ?

Answer 1

Answer:

ANSWER

Given: AB = 12cm, AD =8cm, AB = 12cm and AC = 18cm

To Prove: DE∥BC

in ∆ABC,

DB

AD

=

AB−AD

AD

=

12−8

8

=2

And AEAC=

AC−EC

AE

=

18−12

12

=2

Then,

DB

AD

=

EC

AE

Basic Proportionality theorem which states that

if a line is drawn parallel to one side of a triangle the other two sides in distinct points, then the other two sides are divided in the same ratio.

Hence, DE∥BC

[by converse of basic

proportionality theorem]

Hence, Proved

Hope it will help you