Thread: DE Parallel to BC?

Given triangle ABC and segment DE, if AD =2, DB =3,
AE =4 and EC =4, is DE parallel to BC?

This is converse of Basic Proportionality Theorem

Originally Posted by magentarita

Given triangle ABC and segment DE, if AD =2, DB =3,
AE =4 and EC =4, is DE parallel to BC?

See diagram.

The "Triangle Proportionality Theroem" states: If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then it separates these sides into segments of proportional length.

So, if , then





Therefore,

Originally Posted by masters

See diagram.

The "Triangle Proportionality Theroem" states: If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then it separates these sides into segments of proportional length.

So, if , then





Therefore,

I thank both replies. I want to thank masters for always answering my questions quickly and professionally.