Final answer:
Triangle ABC is similar to triangle DBE by the angle-angle similarity theorem.
Step-by-step explanation:
To prove that triangle ABC is similar to triangle DBE, we can use the fact that DE is a midsegment of triangle ABC. A midsegment is a line segment that connects the midpoints of two sides of a triangle. In this case, DE connects the midpoints of side AB and side BC.
Since DE is a midsegment, it is parallel to and half the length of side AC. Similarly, triangle DBE is formed by the midpoints of side BD and side BE, so DE is also parallel to and half the length of side DB.
By the midpoint theorem, we know that DE is parallel to AC and DB, and DE is half the length of AC and DB. Therefore, triangle ABC is similar to triangle DBE by the angle-angle similarity theorem.