Answer:
Statement 1. AB/DB = CB/EB
Reason 1: Given
Statement 2: ∠ABC = ∠BDE
Reason 2: Vertical angles
Statement 3: ∆ABC~∆DBE
Reason 3: SAS (side - angle - side)
Explanation:
It is given that AB/DB = CB/EB. So, we can say that the ratio of side AB to DB is equal to the ratio of side CB to EB. This made these sides similar.
Additionally, ∠ABC and ∠BDE are vertical angles because they are opposite angles formed when two lines intersect. Vertical angles have the same measure so, ∠ABC = ∠BDE.
Now, we can say that the triangles ABC and DBE are similar by SAS (Side-Angle-Side). Because two sides are similar and the angle between them is congruent.
Therefore, the answer is
Statement 1. AB/DB = CB/EB
Reason 1: Given
Statement 2: ∠ABC = ∠BDE
Reason 2: Vertical angles
Statement 3: ∆ABC~∆DBE
Reason 3: SAS (side - angle - side)
