Question

If D and E are respectively the points on the side AB and AC of a triangle ABC such that AD = 6 cm, BD = 9 cm, AE = 8 cm and EC = 12 cm, then show that DE || BC.​

Answer 1

Answer:

Given,  

AE =  6 CM

EC = 9 CM  

AD = 8 CM  

DB = 12 CM  

Clearly,

AD/DB = 8/12 =  2/3

and,

AE/ EC = 6/9 = 2/3

Hence,

AE/EC = AD/BD

We know that, if  a line   intersects  two sides  of triangle in same  ratio of sides, Then the intersecting  line  will be half  of  third  side  of  triangle and parallel   to third  side.  

Hence,  

DE || BD  

And,

DE  = 1/2 * BC

BC = 2DE

Answer 2

First prove the converse of BPT theorem to show that the ratio between the sides of two triangles are equal.

AD/BD=AE/EC

6/9=8/12

2/3=2/3

Therefore by converse of BPT,

DE || BC