Question

In ∆ABC shown below, segment is DE is parallel to segment AC.

Answer 1

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
Segment DE P AC---Given

Segment AC is a transversal that intersects two parallel lines.---Conclusion from Statement 1


∆ABC ~ ∆DBE---Angle-Angle (AA) Similarity Postulate
(IMAGE)---Converse of the Side-Side-Side Similarity Theorem


Complete the proof by entering the correct statements and reasons.

Answer 2

(IMAGE) =

Answer 3

There are two blank proof rows between the second proof and this; (∆ABC ~ ∆DBE---Angle-Angle (AA) Similarity Postulate) that need to be filled in.