Test Questions: Classifying Polygons by Midpoint of Diagonals

📚 Quick Study Guide

• 🔍 Parallelogram: Diagonals bisect each other.
• ♦️ Rectangle: Diagonals bisect each other and are congruent.
• 📐 Rhombus: Diagonals bisect each other and are perpendicular.
• 🔲 Square: Diagonals bisect each other, are congruent, and are perpendicular.
• 🪁 Kite: One diagonal is the perpendicular bisector of the other.
• ➗ Midpoint Formula: Given points $(x_1, y_1)$ and $(x_2, y_2)$, the midpoint is $\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$.
• 💡 Key Tip: Use the distance formula and slope to confirm properties like congruence and perpendicularity of the diagonals.

Practice Quiz

1. What type of quadrilateral has diagonals that bisect each other but are not necessarily congruent or perpendicular?
   1. Square
   2. Rectangle
   3. Parallelogram
   4. Rhombus
2. The diagonals of a quadrilateral bisect each other and are congruent. Which of the following must the quadrilateral be?
   1. Rhombus
   2. Square
   3. Rectangle
   4. Parallelogram
3. In quadrilateral ABCD, the midpoint of diagonal AC is (2, 3) and the midpoint of diagonal BD is also (2, 3). What type of quadrilateral could ABCD be?
   1. Trapezoid
   2. Kite
   3. Parallelogram
   4. Isosceles Triangle
4. The diagonals of a quadrilateral are perpendicular bisectors of each other. What is the most specific name for this quadrilateral?
   1. Rectangle
   2. Rhombus
   3. Parallelogram
   4. Trapezoid
5. Quadrilateral EFGH has vertices E(0, 0), F(5, 0), G(5, 5), and H(0, 5). What is the most specific name for this quadrilateral based on its diagonals?
   1. Rectangle
   2. Rhombus
   3. Square
   4. Parallelogram
6. One diagonal of a quadrilateral is the perpendicular bisector of the other. What type of quadrilateral is this?
   1. Parallelogram
   2. Rectangle
   3. Kite
   4. Rhombus
7. The midpoint of both diagonals of a quadrilateral is at the origin (0,0). Which of the following quadrilaterals could it be?
   1. Kite
   2. Trapezoid
   3. Rhombus
   4. Isosceles trapezoid