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Question
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Complete the proof.
Given: AB · BE = CB · BD
Prove: ΔABC ~ ΔDBE
Two triangles A B C and D B E are formed by intersecting segments. Segment A E intersects Segment C D at point B. A segment connects points A and C. Another segment connects points D and E.
A two column proof is shown.First row: Statement 1. A B times B E equals C B times B D Reason 1. Given
Second row: Statement 2 Start Fraction C B over B E End Fraction equals Start Fraction A B over B D End Fraction Reason 2 Property of Question Mark
Third row Statement 3: angle A B C is congruent to angle D B E Reason 3 Question Mark
Fourth row Statement 4: triangle A B C is congruent to triangle D B E Reason 4 Question Mark
(3 points)
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First row: Statement 1. AB · BE = CB · BD Reason 1. Given
Second row: Statement 2. CB/BE = AB/BD Reason 2: Property of ratios
Third row: Statement 3. Angle ABC is congruent to angle DBE Reason 3: Corresponding angles formed by intersecting lines are congruent
Fourth row: Statement 4. Triangle ABC is congruent to triangle DBE Reason 4: SAS (Side-Angle-Side) congruence criteria, where CB/BE = AB/BD, angle ABC is congruent to angle DBE, and line segment AB is congruent to line segment DB.