Q4 of 56 Page 6

In a ΔABC, D and E are points on the sides AB and AC respectively. For AB = 12 cm, AD = 8 cm, AE = 12 cm and AC = 18 cm show that DE||BC.

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AB = 12 cm, AD = 8 cm, and AC = 18 cm.


∴ DB=AB-AD


= 12-8


=4 cm


EC=AC-AE


= 18-12


= 6 cm


Now AD/DB=8/4=2


AE/EC=12/6=2


Thus, DE divides side AB and AC of ⊿ ABC in same ratio


Then by the converse of basic proportionality theorem DE||BC.


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