Question 1210506
This is a great set of questions about the properties of different quadrilaterals!

Here are the answers, with a brief explanation and an image tag for a visual aid.

### 📐 Quadrilateral Properties

| Property | Quadrilateral Type |
| :--- | :--- |
| **Both pairs of opposite sides are parallel.** | * **Parallelogram** * **Rectangle** * **Rhombus** * **Square** |
| **All four sides are equal in length.** | * **Rhombus** * **Square** |
| **All four angles are right angles.** | * **Rectangle** * **Square** |
| **All four sides are equal in length AND all four angles are right angles.** | * **Square** |
| **Exactly one pair of opposite sides is parallel.** | * **Trapezoid** (or **Trapezium** in some regions) |
| **Its diagonals bisect each other.** | * **Parallelogram** * **Rectangle** * **Rhombus** * **Square** |
| **Its diagonals are congruent (equal in length).** | * **Rectangle** * **Square** * **Isosceles Trapezoid** |
| **Its diagonals are perpendicular bisectors of each other.** | * **Rhombus** * **Square** |
| **Its diagonals are perpendicular.** | * **Rhombus** * **Square** * **Kite** |



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### **Detailed Notes on Relationships**

* **Parallelogram:** A quadrilateral with two pairs of parallel sides. All parallelograms have diagonals that bisect each other.
* **Rectangle:** A parallelogram with four right angles. It inherits all parallelogram properties (including diagonals bisecting each other) and adds the property of having congruent diagonals.
* **Rhombus:** A parallelogram with four equal sides. It inherits all parallelogram properties and adds the property of having perpendicular diagonals that are also perpendicular bisectors.
* **Square:** A quadrilateral that is *both* a Rectangle and a Rhombus. It has all the properties listed for both, including four equal sides, four right angles, parallel opposite sides, and diagonals that are congruent, perpendicular, and bisect each other.
* **Trapezoid:** Has exactly one pair of parallel sides.
* **Kite:** Has two distinct pairs of equal-length adjacent sides. Its diagonals are perpendicular.

Would you like to explore the properties of a specific quadrilateral in more detail, like the kite or an isosceles trapezoid?