10 Free Printable Properties of Quadrilaterals Worksheets - Free Printable

The image you've uploaded is a "Properties of Quadrilateral Worksheet" from *Math Monks*. It's a chart that lists various properties of six types of quadrilaterals: Parallelogram, Rectangle, Square, Trapezoid, Isosceles Trapezoid, and Kite.

You are asked to complete the table by checking (✓) which properties apply to each quadrilateral. The worksheet already has some checks filled in, but there are several blank cells that need to be completed based on geometric properties.

Let’s go through each property and fill in the missing information for all quadrilaterals.

---

✔ Step-by-Step Explanation & Completion

We’ll analyze each row (property) and determine which quadrilaterals satisfy it.

---

#### 1. Sketch the given Quadrilateral
Already provided — no action needed.

---

#### 2. Opposite sides parallel
- Parallelogram: ✓ (by definition)
- Rectangle: ✓ (a type of parallelogram)
- Square: ✓ (a type of rectangle and parallelogram)
- Trapezoid: ✗ (only one pair of opposite sides parallel)
- Isosceles Trapezoid: ✗ (same as trapezoid – only one pair parallel)
- Kite: ✗ (no opposite sides necessarily parallel)

✔ So, only parallelogram, rectangle, square have this property.

---

#### 3. Opposite sides congruent
- Parallelogram: ✓
- Rectangle: ✓
- Square: ✓
- Trapezoid: ✗ (not generally true)
- Isosceles Trapezoid: ✗ (only the non-parallel sides are congruent, not opposite sides)
- Kite: ✗ (adjacent sides are congruent, not opposite)

✔ Only parallelogram, rectangle, square have opposite sides congruent.

---

#### 4. Two pairs of opposite sides congruent
- This means both pairs of opposite sides are equal in length.
- Same as above: Parallelogram, Rectangle, Square → ✓
- Trapezoid: ✗
- Isosceles Trapezoid: ✗ (only legs are congruent, but not opposite sides)
- Kite: ✗ (two adjacent sides are congruent, not opposite)

✔ So same as above: Parallelogram, Rectangle, Square → ✓

---

#### 5. Opposite angles congruent
- Parallelogram: ✓ (opposite angles are equal)
- Rectangle: ✓ (all angles are 90°)
- Square: ✓ (all angles are 90°)
- Trapezoid: ✗ (no general rule)
- Isosceles Trapezoid: ✗ (base angles are congruent, but opposite angles are not necessarily equal)
- Kite: ✗ (only one pair of opposite angles may be equal, not guaranteed)

✔ So only parallelogram, rectangle, square → ✓

---

#### 6. Diagonals are congruent
- Parallelogram: ✗ (diagonals are not necessarily congruent)
- Rectangle: ✓ (diagonals are congruent)
- Square: ✓ (diagonals are congruent)
- Trapezoid: ✗ (not generally)
- Isosceles Trapezoid: ✓ (this is a key property!)
- Kite: ✗ (diagonals are not congruent unless it's a special case)

✔ So:
- Rectangle, Square, Isosceles Trapezoid → ✓

> Note: In an isosceles trapezoid, diagonals are congruent.

---

#### 7. Diagonals bisect each other
- Parallelogram: ✓ (yes)
- Rectangle: ✓ (yes, since it's a parallelogram)
- Square: ✓ (yes)
- Trapezoid: ✗ (diagonals do not bisect each other)
- Isosceles Trapezoid: ✗ (they don't bisect each other)
- Kite: ✗ (only one diagonal is bisected, not both)

✔ So only parallelogram, rectangle, square → ✓

---

#### 8. Four sides congruent
- Parallelogram: ✗ (not necessarily)
- Rectangle: ✗ (sides come in two pairs, not all equal)
- Square: ✓ (all four sides equal)
- Trapezoid: ✗
- Isosceles Trapezoid: ✗
- Kite: ✗ (two pairs of adjacent sides equal, not all four)

✔ Only Square → ✓

> Note: A rhombus has four congruent sides, but it's not listed here.

---

#### 9. Four right angles
- Parallelogram: ✗
- Rectangle: ✓
- Square: ✓
- Trapezoid: ✗
- Isosceles Trapezoid: ✗
- Kite: ✗

✔ Only Rectangle, Square → ✓

---

✔ Final Completed Table:

| Property | Parallelogram | Rectangle | Square | Trapezoid | Isosceles Trapezoid | Kite |
|--------|----------------|-----------|--------|-----------|----------------------|------|
| Sketch | ✔ | ✔ | ✔ | ✔ | ✔ | ✔ |
| 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 | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ |

---

🔍 Summary of Key Properties:

| Shape | Key Properties |
|-------|----------------|
| Parallelogram | Opposite sides parallel, opposite sides congruent, opposite angles congruent, diagonals bisect each other |
| Rectangle | All parallelogram properties + diagonals congruent + four right angles |
| Square | All rectangle properties + four sides congruent |
| Trapezoid | One pair of opposite sides parallel (no others) |
| Isosceles Trapezoid | One pair of opposite sides parallel + legs congruent + diagonals congruent |
| Kite | Two pairs of adjacent sides congruent, one diagonal bisected, one pair of opposite angles congruent |

---

✔ Final Answer:

The worksheet should be completed with the following additional checks (in blue):

- Diagonals are congruent → add ✓ in Rectangle, Square, Isosceles Trapezoid
- Four sides congruent → add ✓ only in Square
- Four right angles → add ✓ in Rectangle, Square

All other columns are already correctly filled.

> 🟩 Note: The original worksheet has some errors or omissions. For example, kites do not have opposite sides parallel or congruent, nor do they have diagonals that bisect each other (only one does), so those are left blank.

---

Let me know if you'd like this as a printable version or want explanations for any specific shape!