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Answered

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

Choices for first ?:

  • AD
  • DE

Choices for second ?:

  • FG

-BC

If AD/DB = AE/EC, then line segment (?) is parallel to line segment (?) . Choices for first ?: - AD - DE Choices for second ?: - FG -BC class=

Verified Answer :

JeanaShupp

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 .

boffeemadrid

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 .

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