Question

In ������ABC shown below, segment DE is parallel to segment AC:

Triangles ABC and DBE where DE is parallel to AC

The two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally:

Statement Reason
1. Line segment DE is parallel to line segment AC 1. Given
2. Line segment AB is a transversal that intersects two parallel lines. 2. Conclusion from Statement 1.
3. 3.
4. 4.
5. ������ABC ~ ������DBE 5. Angle-Angle (AA) Similarity Postulate
6. BD over BA equals BE over BC 6.

Answer 1

@briananicolenelson

Answer 2

@confluxepic

Answer 3

@undeadknight26