Question

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

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

The following flowchart 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 2, space labeled 1 occurs. By Converse of the Corresponding An

Answer 1

@mathstudent55 @math&ing001

Answer 2

@math&ing001

Answer 3

@AbbyWuvsChu @Ashleyrh1999 @Christian_10_

Answer 4

@Callisto

Answer 5

@imqwerty