Final answer:
The missing reason in the flowchart proof is likely the Triangle Proportionality Theorem, which states that a line dividing two sides of a triangle proportionally is parallel to the third side.
Step-by-step explanation:
The given geometric problem involves proving that a line which divides two sides of a triangle proportionally is parallel to the third side. The missing reasoning in the proof for this claim is likely related to the Triangle Proportionality Theorem or basic Euclidean geometric principles such as similar triangles or parallel line theorems. The theorem states that if a line divides two sides of a triangle proportionally, then it must be parallel to the third side. Therefore, to complete the flowchart proof and provide the missing reason, one would typically reference the Triangle Proportionality Theorem or the corresponding axiom or postulate related to it.
Triangle Proportionality Theorem often serves as the keystone for solving this type of problem, and the given condition that BD/BA = BE/BC is a direct application of this theorem. Once the concept is applied, the conclusion that line DE is parallel to side AC naturally follows from the theorem.