4. In each of the following, choose at least one word from parallelogram, rectangle,
   rhombus, trapezoid, kite, or square, so that the resulting sentence is true. If none of
   the words makes the sentence true, answer “none.”
   a quadrilateral whose diagonals are equal and bisect each other.
   b. a quadrilateral whose diagonals are perpendicular and bisects each
   b. ather.
   a quadrilateral whose diagonals are equal, perpendicular and they
   d. other

a. A quadrilateral whose diagonals are equal and bisect each other.

• Parallelogram: Yes, the diagonals bisect each other, but they are not necessarily equal.
• Rectangle: Yes, the diagonals are equal and bisect each other.
• Rhombus: Yes, the diagonals bisect each other, but they are not equal.
• Trapezoid: No, this does not apply.
• Kite: No, this does not apply.
• Square: Yes, a square is a special case of a rectangle and a rhombus.

b. A quadrilateral whose diagonals are perpendicular and bisect each other.

• Parallelogram: No, the diagonals do not have to be perpendicular.
• Rectangle: No, the diagonals are not perpendicular.
• Rhombus: Yes, the diagonals are perpendicular and bisect each other.
• Trapezoid: No, this does not apply.
• Kite: Yes, the diagonals are perpendicular, but they do not necessarily bisect each other.
• Square: Yes, a square is a special case of a rhombus.

c. A quadrilateral whose diagonals are equal, perpendicular, and they bisect each other.

• Parallelogram: No, the diagonals are not necessarily equal.
• Rectangle: No, the diagonals are equal but not perpendicular.
• Rhombus: Yes, the diagonals are perpendicular and bisect each other, but they are not equal.
• Trapezoid: No, this does not apply.
• Kite: Yes, the diagonals are perpendicular, but they are not equal.
• Square: Yes, a square meets all these conditions.

Summary of Answers:

• a. Rectangle (or Square)
• b. Rhombus (or Square)
• c. Square