Given: In ∆ABC below,BD over BA equals BE over BC .
Prove: segment DE is parallel to segment AC
Triangles ABC and DBE where BD is to BA as BE is to BC.

The flow chart proof with missing statements and reasons proves that if a line intersects two sides of a triangle and divides these sides proportionally, the line is parallel to the third side.

Top path, by Given the ratio of line segments BD to BA is equal to the ratio of line segments BE to BC; by Side-Angle-Side Similarity Postulate, triangle ABC is similar to triangle DBE; by space labeled by 2, space labeled by 1 occurs; by Convers

Question

Given: In ∆ABC below,BD over BA equals BE over BC .
Prove: segment DE is parallel to segment AC
Triangles ABC and DBE where BD is to BA as BE is to BC.

The flow chart proof with missing statements and reasons proves that if a line intersects two sides of a triangle and divides these sides proportionally, the line is parallel to the third side.

Top path, by Given the ratio of line segments BD to BA is equal to the ratio of line segments BE to BC; by Side-Angle-Side Similarity Postulate, triangle ABC is similar to triangle DBE; by space labeled by 2, space labeled by 1 occurs; by Convers