If ad/db = ae/ec, then line segment is parallel to line segment .
choices for first ? :
- ad
- de

choices for second ? :
- fg
-bc

Step-by-step explanation:

In ΔABC, we have

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 , 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  ,then line segment DE is parallel to line segment BC .

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 .