Question

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

Choices for first ?:
- AD
- DE

Choices for second ?:
- FG
-BC

Answer 1

Explanation:

In ΔABC, we have

`(AD)/(DB)=(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
`(AD)/(DB)=(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
`(AD)/(DB)=(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.

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 .