Q. 114.2( 5 Votes )

If D and E are points on sides AB and AC respectively of ΔABC and AB = 12 cm, AD = 8 cm, AE = 12 cm, AC =18 cm, then prove that DE || BC.

Answer :


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


To Prove: DE || BC


In ABC,





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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