1. **Problem statement:** Given rectangle ABCD with diagonal BD, trace lines D₁ and D₂ perpendicular to BD at points A and C respectively. 2. **Recall:** In a rectangle, diagonals are equal and bisect each other. Lines perpendicular to the same line at different points are parallel. 3. **Step 1: Understand the rectangle and diagonal BD.** Since ABCD is a rectangle, BD is a diagonal connecting B and D. 4. **Step 2: Draw line D₁ perpendicular to BD at A.** By definition, D₁ is perpendicular to BD at point A. 5. **Step 3: Draw line D₂ perpendicular to BD at C.** Similarly, D₂ is perpendicular to BD at point C. 6. **Step 4: Determine the relative position of D₁ and D₂.** Since both D₁ and D₂ are perpendicular to the same line BD, they are parallel to each other. 7. **Justification:** - (D₁) ⟂ (BD) since it is constructed perpendicular at A. - (D₂) ⟂ (BD) since it is constructed perpendicular at C. - Two lines perpendicular to the same line are parallel. **Final answer:** Lines (D₁) and (D₂) are parallel.