Properties of quadrilaterals chart showing which shapes have 4 sides, parallel sides, right angles, and equal sides.

You’ve uploaded a quadrilateral classification chart that shows which types of quadrilaterals satisfy certain geometric properties. The goal is to understand and verify the checkmarks (✓) in each cell based on the definitions of the shapes.

Let’s go row by row and column by column to explain why each checkmark is or isn’t there.

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## 🔷 Column 1: “4 sides and 4 angles”
✔ All quadrilaterals have 4 sides and 4 angles — that’s the definition of a quadrilateral!

- Quadrilateral → ✓ (by definition)
- Trapezoid → ✓ (a type of quadrilateral)
- Parallelogram → ✓
- Rectangle → ✓
- Rhombus → ✓
- Square → ✓

✔️ All checkmarks are correct here.

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## 🔷 Column 2: “At least one set of parallel sides”

This means at least one pair of opposite sides is parallel.

- Quadrilateral → ✘ *Not all quadrilaterals have parallel sides!*
➤ Example: A kite or an irregular quadrilateral may have no parallel sides.
⚠️ The checkmark here is INCORRECT.

- Trapezoid → ✓ (By definition, a trapezoid has at least one pair of parallel sides — in some regions, it’s defined as exactly one pair; in others, at least one. In this chart, they’re using the “at least one” definition.)

- Parallelogram → ✓ (Has two pairs, so definitely satisfies “at least one”)

- Rectangle → ✓ (Also a parallelogram)

- Rhombus → ✓ (Also a parallelogram)

- Square → ✓ (Also a parallelogram)

✔ So only the Quadrilateral row should NOT have a checkmark here.

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## 🔷 Column 3: “2 sets of parallel sides”

This means two pairs of opposite sides are parallel — i.e., a parallelogram.

- Quadrilateral → ✘ (No — not necessarily)
- Trapezoid → ✘ (Only has one pair — unless it’s a parallelogram, but typically trapezoids are defined as having *exactly* one pair. In this chart, since Trapezoid only has one check in col 2, it’s likely defined as *exactly* one pair.)
- Parallelogram → ✓ (Definition!)
- Rectangle → ✓ (Special parallelogram)
- Rhombus → ✓ (Special parallelogram)
- Square → ✓ (Special parallelogram)

✔ All checkmarks are correct here.

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## 🔷 Column 4: “4 right angles”

This means all interior angles = 90°.

- Quadrilateral → ✘ (No — most don’t)
- Trapezoid → ✘ (Usually doesn’t — unless it’s a rectangle, but then it wouldn’t be just a trapezoid)
- Parallelogram → ✘ (Opposite angles equal, but not necessarily 90°)
- Rectangle → ✓ (Definition: parallelogram with 4 right angles)
- Rhombus → ✘ (All sides equal, but angles can be non-right — e.g., a diamond shape)
- Square → ✓ (Has 4 right angles)

⚠️ Rhombus should NOT have a checkmark here.
➡️ *The checkmark in Rhombus row, column 4 is INCORRECT.*

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## 🔷 Column 5: “4 equal sides”

All sides are congruent.

- Quadrilateral → ✘ (No — too general)
- Trapezoid → ✘ (Usually not — unless it’s a rhombus, but then it’s not just a trapezoid)
- Parallelogram → ✘ (Opposite sides equal, but not necessarily all four)
- Rectangle → ✘ (Opposite sides equal, but adjacent sides may differ — unless it’s a square)
- Rhombus → ✓ (Definition: parallelogram with 4 equal sides)
- Square → ✓ (Also has 4 equal sides)

✔ All checkmarks correct here.

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## 🔷 Column 6: “4 right angles and 4 equal sides”

This is the definition of a square.

- Quadrilateral → ✘
- Trapezoid → ✘
- Parallelogram → ✘
- Rectangle → ✘ (Has 4 right angles, but not necessarily 4 equal sides)
- Rhombus → ✘ (Has 4 equal sides, but not necessarily 4 right angles)
- Square → ✓ (Yes — combines both properties)

✔ Only Square should have a checkmark here — and it does. ✔️

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## ✔ Summary of Corrections Needed:

| Shape | Column 2 (“At least one set of parallel sides”) | Column 4 (“4 right angles”) |
|---------------|--------------------------------------------------|-----------------------------|
| Quadrilateral | ✘ Should be unchecked | — |
| Rhombus | — | ✘ Should be unchecked |

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## 📝 Final Corrected Chart (Text Version):

```
4 sides & 4 angles | At least one set of parallel sides | 2 sets of parallel sides | 4 right angles | 4 equal sides | 4 right angles & 4 equal sides
------------------------------------------------------------------------------------------------------------
Quadrilateral ✓ ✗ (should be unchecked) ✗ ✗ ✗ ✗
Trapezoid ✓ ✓ ✗ ✗ ✗ ✗
Parallelogram ✓ ✓ ✓ ✗ ✗ ✗
Rectangle ✓ ✓ ✓ ✓ ✗ ✗
Rhombus ✓ ✓ ✓ ✗ (should be unchecked) ✓ ✗
Square ✓ ✓ ✓ ✓ ✓ ✓
```

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## 💡 Key Takeaways:

- All quadrilaterals have 4 sides and 4 angles, but not all have parallel sides or right angles.
- Trapezoid: Has *at least one* pair of parallel sides (in this chart’s definition).
- Parallelogram: Has *two* pairs of parallel sides.
- Rectangle: Parallelogram + 4 right angles.
- Rhombus: Parallelogram + 4 equal sides.
- Square: Rectangle + Rhombus → 4 right angles + 4 equal sides.

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✔ So, the chart is mostly correct — but two errors need fixing:
1. Remove the check from Quadrilateral under “At least one set of parallel sides”.
2. Remove the check from Rhombus under “4 right angles”.

Let me know if you’d like a visual corrected version!