Question

If AD/DB = AE/EC, then line segment (?) is parallel to line segment (?) .

Answer 1

Answer:

Step-by-step explanation:

In ΔABC, we have

$\frac{AD}{DB}=\frac{AE}{EC}$

The Converse of the basic proportionality theorem states that if a line divides two sides of a triangle in same ratio then the line must be parallel to the third side.

Now, it is given that $\frac{AD}{DB}=\frac{AE}{EC}$, this implies that line segment DE divides AB and AC in the same ratio.

Thus, by converse of basic proportionality theorem  

line segment DE= line segment BC.

Therefore, if  $\frac{AD}{DB}=\frac{AE}{EC}$,then line segment DE is parallel to line segment BC .

Answer 2

Answer: 1) DE and 2) BC

If AD/DB = AE/EC, then line segment DE is parallel to line segment BC.

Step-by-step explanation:

Given : In triangle ABC

AD/DB = AE/EC

⇒ line segment DE dividing AB and AC in same ratio.

Therefore by converse of basic proportionality theorem

line segment DE= line segment BC

Converse of basic proportionality theorem states that if a line divides two sides of a triangle in same ratio then the line must be parallel to the third side.

Hence, If AD/DB = AE/EC, then line segment DE is parallel to line segment BC .