In a given ∆ ABC , D and E are points on the sides AB and AC respectively. If AB = 12cm , AD = 8cm
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Step-by-step explanation:
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.
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