In ΔABC shown below, BD over BA equals BE over BC:

Triangle ABC with segment DE intersecting sides AB and BC respectively.

flowchart proof with missing statements and reasons proves 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 Converse of the Corresponding Angles Postu

Question

In ΔABC shown below, BD over BA equals BE over BC:

Triangle ABC with segment DE intersecting sides AB and BC respectively.

flowchart proof with missing statements and reasons proves 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 Converse of the Corresponding Angles Postu