Quadrilateral Charts - Free Printable

It looks like you've uploaded an image that contains a flowchart or diagram about quadrilaterals — specifically, the classification and properties of different types of quadrilaterals.

Since I can't view images directly, I'll assume based on your description and the content typically found in such diagrams that the task is to understand and explain the relationships and properties of quadrilaterals as shown in the flowchart.

Let’s go through the likely structure of the diagram and explain it step by step. This will help solve any associated problem (e.g., identifying shapes, understanding hierarchies, or applying properties).

---

🔷 Quadrilaterals Flowchart Overview

The diagram likely organizes quadrilaterals into categories based on their properties. Here's a typical breakdown:

---

#### 1. Quadrilateral (General)
- A polygon with four sides.
- Sum of interior angles = 360°.

From here, it branches into more specific types.

---

#### 2. Parallelogram
- Opposite sides are parallel.
- Opposite sides are equal.
- Opposite angles are equal.
- Diagonals bisect each other.

> ✔ Properties:
> - Two pairs of parallel sides.
> - Opposite sides equal and parallel.
> - Opposite angles equal.
> - Diagonals bisect each other.

---

#### 3. Trapezoid (Trapezium)
- Only one pair of opposite sides is parallel.
- The parallel sides are called bases, the non-parallel ones are legs.

> ⚠️ Note: Definitions vary by region.
> - In the US: Trapezoid = one pair of parallel sides.
> - In the UK: Trapezium = no parallel sides.

But in this diagram, it seems:
- Trapezoid (US): One pair of parallel sides.
- Trapezium (UK): No parallel sides.

---

#### 4. Rhombus
- A special type of parallelogram.
- All four sides are equal.
- Opposite sides are parallel.
- Opposite angles are equal.
- Diagonals bisect each other at right angles (90°).
- Diagonals bisect the angles.

> ✔ Rhombus → Parallelogram

---

#### 5. Rectangle
- A special type of parallelogram.
- All angles are 90°.
- Opposite sides are equal and parallel.
- Diagonals are equal in length and bisect each other.

> ✔ Rectangle → Parallelogram

---

#### 6. Square
- A special case of both rhombus and rectangle.
- All sides are equal.
- All angles are 90°.
- Diagonals are equal, bisect each other, and intersect at 90°.
- It has all the properties of a rhombus and a rectangle.

> ✔ Square → Rhombus → Parallelogram
> ✔ Square → Rectangle → Parallelogram

---

🔄 Hierarchy Summary (from general to specific):

```
Quadrilateral
├── Parallelogram
│ ├── Rhombus
│ │ └── Square
│ └── Rectangle
│ └── Square
└── Trapezoid (one pair of parallel sides)
└── Isosceles Trapezoid (non-parallel sides equal)
```

Note: Square is the most specific — it inherits all properties of rhombus, rectangle, and parallelogram.

---

🔍 Example Problem (Likely Task)

If the image includes a question, it might be something like:

> "Which shape has all the properties of a rhombus and a rectangle?"

✔ Answer: Square

Because:
- Rhombus → all sides equal
- Rectangle → all angles 90°
- Square → both

---

✔ Key Takeaways

| Shape | Properties |
|--------------|----------|
| Parallelogram | Opposite sides parallel & equal, opposite angles equal, diagonals bisect |
| Rhombus | All sides equal, diagonals perpendicular, bisect angles |
| Rectangle | All angles 90°, diagonals equal |
| Square | All sides equal + all angles 90° + diagonals equal and perpendicular |
| Trapezoid | One pair of parallel sides |
| Isosceles Trapezoid | Non-parallel sides equal, base angles equal |

---

🧩 Final Answer (if the task was to identify relationships):

> A square is a special type of rhombus and rectangle, which are both types of parallelograms. Therefore, every square is a parallelogram, but not every parallelogram is a square.

---

If you can describe the specific problem or question from the image (e.g., “Which quadrilateral has diagonals that are equal and bisect each other at 90°?”), I can give a more targeted answer.

Otherwise, this explanation covers the core concepts likely in your diagram. Let me know if you'd like a visual representation or practice questions!