Free Printable Properties of Quadrilaterals Worksheets - Free Printable

The image you've uploaded is a "Properties of Quadrilateral Worksheet" from Math Monks, which asks students to fill in a chart comparing the properties of different quadrilaterals: Parallelogram, Rectangle, Square, Trapezoid, Isosceles Trapezoid, and Kite.

You've already filled in some of the checks (✓) for various properties. Let's go through each property and complete the missing information based on geometric definitions and relationships among quadrilaterals.

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✔ Step-by-step Explanation & Completion

We'll analyze each row and fill in the correct checkmarks (✓) where applicable.

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#### 1. Sketch the given Quadrilateral
✔ Already done — sketches are provided.

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#### 2. Opposite sides parallel

| Shape | Check? |
|-------|--------|
| Parallelogram | ✓ |
| Rectangle | ✓ |
| Square | ✓ |
| Trapezoid | ✘ Only one pair of opposite sides parallel |
| Isosceles Trapezoid | ✓ (only one pair, but it's a special trapezoid) |
| Kite | ✘ |

> ✔ Trapezoid: By definition, exactly one pair of opposite sides is parallel. So not both pairs → no check.
>
> ✔ Isosceles Trapezoid: Still only one pair of opposite sides parallel → no check for "opposite sides parallel" unless specified as two pairs.

But wait — the column says "Opposite sides parallel", meaning both pairs must be parallel.

So:
- Trapezoid: ✘
- Isosceles Trapezoid: ✘
- Kite: ✘

✔️ Final: Only parallelogram, rectangle, square have both pairs of opposite sides parallel.

> ✔ So Trapezoid, Isosceles Trapezoid, Kite get no check here.

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#### 3. Opposite sides congruent

| Shape | Check? |
|-------|--------|
| Parallelogram | ✓ |
| Rectangle | ✓ |
| Square | ✓ |
| Trapezoid | ✘ |
| Isosceles Trapezoid | ✘ (only non-parallel sides are congruent) |
| Kite | ✘ |

> ✔ Only parallelograms, rectangles, squares have both pairs of opposite sides congruent.
>
> - In a trapezoid, only one pair of sides is parallel; opposite sides are not necessarily congruent.
> - In an isosceles trapezoid, the legs (non-parallel sides) are congruent, but opposite sides (top/bottom, left/right) are not.
> - A kite has two pairs of adjacent sides congruent, not opposite.

✘ So Trapezoid, Isosceles Trapezoid, Kite do not have opposite sides congruent.

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#### 4. Two pairs of opposite sides congruent

This is the same as above — means both pairs of opposite sides are equal in length.

So same result:
- Parallelogram: ✓
- Rectangle: ✓
- Square: ✓
- Trapezoid: ✘
- Isosceles Trapezoid: ✘
- Kite: ✘

> Note: Kite has two pairs of adjacent sides congruent, not opposite.

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#### 5. Opposite angles congruent

| Shape | Check? |
|-------|--------|
| Parallelogram | ✓ |
| Rectangle | ✓ |
| Square | ✓ |
| Trapezoid | ✘ |
| Isosceles Trapezoid | ✔ Yes! Base angles are congruent → opposite angles are not necessarily equal.
| Kite | ✘ |

Wait — let’s clarify:

- Parallelogram: Opposite angles are congruent → ✓
- Rectangle: All angles 90° → opposite angles congruent → ✓
- Square: Same → ✓
- Trapezoid: Not guaranteed → ✘
- Isosceles Trapezoid: Base angles are congruent, but opposite angles are supplementary, not necessarily congruent. For example, if base angles are 70° and 110°, then opposite angles are 70° and 110° → not congruent → ✘
- Kite: One pair of opposite angles are congruent (the ones between unequal sides), but not both pairs → so not all opposite angles congruent → ✘

> So only parallelogram, rectangle, square have opposite angles congruent.

✔ So: Trapezoid, Isosceles Trapezoid, Kite → ✘

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#### 6. Diagonals are congruent

| Shape | Check? |
|-------|--------|
| Parallelogram | ✘ |
| Rectangle | ✓ |
| Square | ✓ |
| Trapezoid | ✘ |
| Isosceles Trapezoid | ✓ |
| Kite | ✘ |

> ✔ Rectangle: Diagonals are congruent → ✓
> ✔ Square: Also a rectangle → ✓
> ✔ Isosceles Trapezoid: Diagonals are congruent → ✓
> ✘ Parallelogram: Diagonals are not necessarily congruent (unless it's a rectangle)
> ✘ Trapezoid: General trapezoid doesn’t have congruent diagonals
> ✘ Kite: Diagonals are not congruent — one is bisected, the other is longer/shorter

So add:
- Isosceles Trapezoid: ✓
- Others: already marked correctly

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#### 7. Diagonals bisect each other

| Shape | Check? |
|-------|--------|
| Parallelogram | ✓ |
| Rectangle | ✓ |
| Square | ✓ |
| Trapezoid | ✘ |
| Isosceles Trapezoid | ✘ |
| Kite | ✘ |

> ✔ Only parallelograms, rectangles, squares have diagonals that bisect each other.
>
> - Trapezoid: Diagonals do not bisect each other.
> - Isosceles Trapezoid: Diagonals are congruent but do not bisect each other.
> - Kite: One diagonal is bisected, but not both — diagonals do not bisect each other.

So:
- Add: None needed — already correct.

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#### 8. Four sides congruent

| Shape | Check? |
|-------|--------|
| Parallelogram | ✘ |
| Rectangle | ✘ |
| Square | ✓ |
| Trapezoid | ✘ |
| Isosceles Trapezoid | ✘ |
| Kite | ✘ |

> ✔ Only square has all four sides congruent.
>
> - Rhombus would have this, but it's not listed.
> - Kite: Two pairs of adjacent sides congruent → not all four.
> - Trapezoid: No.

So only Square gets ✓

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#### 9. Four right angles

| Shape | Check? |
|-------|--------|
| Parallelogram | ✘ |
| Rectangle | ✓ |
| Square | ✓ |
| Trapezoid | ✘ |
| Isosceles Trapezoid | ✘ |
| Kite | ✘ |

> ✔ Only rectangle and square have four right angles.
>
> - Square is a special rectangle → ✓
> - Others: No

So:
- Rectangle: ✓
- Square: ✓
- Others: ✘

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✔ Final Completed Table

Let’s now fill in all the missing cells with correct marks.

| Quadrilateral Property Chart | Parallelogram | Rectangle | Square | Trapezoid | Isosceles Trapezoid | Kite |
|------------------------------|---------------|-----------|--------|-----------|---------------------|------|
| Sketch the given Quadrilateral | ✔ | ✔ | ✔ | ✔ | ✔ | ✔ |
| Opposite sides parallel | ✓ | ✓ | ✓ | ✘ | ✘ | ✘ |
| Opposite sides congruent | ✓ | ✓ | ✓ | ✘ | ✘ | ✘ |
| Two pairs of opposite sides congruent | ✓ | ✓ | ✓ | ✘ | ✘ | ✘ |
| Opposite angles congruent | ✓ | ✓ | ✓ | ✘ | ✘ | ✘ |
| Diagonals are congruent | ✘ | ✓ | ✓ | ✘ | ✓ | ✘ |
| Diagonals bisect each other | ✓ | ✓ | ✓ | ✘ | ✘ | ✘ |
| Four sides congruent | ✘ | ✘ | ✓ | ✘ | ✘ | ✘ |
| Four right angles | ✘ | ✓ | ✓ | ✘ | ✘ | ✘ |

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🔍 Summary of Key Concepts

| Shape | Special Properties |
|-------|--------------------|
| Parallelogram | Opposite sides parallel & congruent, opposite angles congruent, diagonals bisect each other |
| Rectangle | All properties of parallelogram + diagonals congruent + four right angles |
| Square | All properties of rectangle + all sides congruent |
| Trapezoid | Exactly one pair of opposite sides parallel |
| Isosceles Trapezoid | Non-parallel sides congruent, base angles congruent, diagonals congruent |
| Kite | Two pairs of adjacent sides congruent, one diagonal is perpendicular bisector, one pair of opposite angles congruent |

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✔ Conclusion

Your original worksheet had some checks missing — particularly for Isosceles Trapezoid (diagonals congruent) and Kite (none of the key properties except possibly one angle).

But based on standard geometry definitions, the completed table above is accurate.

Let me know if you'd like a printable version or explanation of any specific shape!