To solve the questions provided, I'll analyze the formulas suitable for each condition:

1. A trapezoid has one pair of parallel sides:

   • Use the Slope Formula. By calculating the slopes of opposite sides, you can prove that one pair has the same slope, indicating they are parallel.

2. The diagonals of a rhombus bisect each other:

   • Use the Midpoint Formula. By finding the midpoints of the diagonals, you can confirm that both diagonals share the same midpoint, proving they bisect each other.

3. The diagonals of a square are congruent:

   • Use the Distance Formula. By calculating the lengths of the diagonals, you can show that they are equal in length, proving congruence.

4. A rectangle has four right angles:

   • Use the Slope Formula. By verifying the slopes of adjacent sides, you can prove they are perpendicular (product of slopes = -1), confirming the angles are 90 degrees.

Would you like further clarification or examples? Here are five related questions for practice:

1. How can you verify a parallelogram using the midpoint formula?
2. What is the role of the distance formula in proving an isosceles triangle?
3. Can the slope formula prove that a quadrilateral is a parallelogram?
4. How would you use these formulas to confirm a kite's properties?
5. How do you confirm that the diagonals of a rectangle bisect each other?

Tip: Always draw a diagram to visualize how the formulas apply to the shape in question!