Free Printable Properties of Quadrilaterals Worksheets - Free Printable

You're correct — the worksheet is asking you to complete the table by marking which properties apply to each type of quadrilateral: Parallelogram, Rectangle, Square, Trapezoid, Isosceles Trapezoid, and Kite.

Some cells are already filled in (with checkmarks), but many are blank. Let’s go row by row and fill in the missing checkmarks based on the geometric definitions and properties of each quadrilateral.

---

✔ Definitions Recap:

- Parallelogram: Opposite sides parallel and congruent; opposite angles congruent; diagonals bisect each other.
- Rectangle: A parallelogram with 4 right angles; diagonals are congruent.
- Square: A rectangle AND a rhombus → all sides congruent, all angles 90°, diagonals congruent and bisect each other at 90°.
- Trapezoid: At least one pair of opposite sides parallel (US definition).
- Isosceles Trapezoid: A trapezoid with non-parallel sides congruent; base angles congruent; diagonals congruent.
- Kite: Two distinct pairs of adjacent sides congruent; one diagonal bisects the other at 90°; one pair of opposite angles congruent.

---

## 🔍 Let's complete the table row by row:

---

Row 1: “Sketch the given Quadrilateral”

→ Already drawn correctly. No action needed.

---

Row 2: “Opposite sides parallel”

✔ Parallelogram – ✔️ (given)
✔ Rectangle – ✔️ (given)
✔ Square – ✔️ (given)
✘ Trapezoid – Only one pair of opposite sides parallel → So NO for "opposite sides parallel" if interpreted as *both pairs*. But wait — the term "opposite sides parallel" can be ambiguous.

> ⚠️ Clarification: In standard math, “opposite sides parallel” usually means both pairs are parallel — which defines a parallelogram. A trapezoid has only one pair of parallel sides, so it does not satisfy “opposite sides parallel” in the plural sense.

So:
- Trapezoid → ✘
- Isosceles Trapezoid → ✘ (still only one pair parallel)
- Kite → ✘ (no requirement for parallel sides)

✔ Final: Only Parallelogram, Rectangle, Square have both pairs of opposite sides parallel.

---

Row 3: “Opposite sides congruent”

✔ Parallelogram – ✔️ (given)
✔ Rectangle – ✔️ (given)
✔ Square – ✔️ (given)
✘ Trapezoid – Not necessarily → ✘
✘ Isosceles Trapezoid – Only the legs (non-parallel sides) are congruent, not the bases → ✘
✔ Kite – Adjacent sides congruent, not opposite → ✘

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

✔ So only Parallelogram, Rectangle, Square.

---

Row 4: “Two pairs of opposite sides congruent”

This is equivalent to saying “opposite sides congruent” — since if both pairs are congruent, then opposite sides are congruent.

✔ Same as above: Parallelogram, Rectangle, Square → ✔️ (already checked)

Trapezoid, Isosceles Trapezoid, Kite → ✘

---

Row 5: “Opposite angles congruent”

✔ Parallelogram – ✔️ (given)
✔ Rectangle – ✔️ (given)
✔ Square – ✔️ (given)
✘ Trapezoid – Not necessarily → ✘
✔ Isosceles Trapezoid – Base angles are congruent, but not opposite angles → ✘
✔ Kite – One pair of opposite angles are congruent (the ones between unequal sides) → ✔️

> 🎯 Important: In a kite, the angles between the unequal sides are congruent — those are opposite angles. So yes, kites have one pair of opposite angles congruent.

✔ So: Parallelogram, Rectangle, Square, Kite

---

Row 6: “Diagonals are congruent”

✔ Parallelogram – Not necessarily → ✘
✔ Rectangle – ✔️ (given)
✔ Square – ✔️ (given)
✘ Trapezoid – Not necessarily → ✘
✔ Isosceles Trapezoid – ✔️ (given)
✘ Kite – Diagonals are perpendicular, but not necessarily congruent → ✘

✔ So: Rectangle, Square, Isosceles Trapezoid

---

Row 7: “Diagonals bisect each other”

✔ Parallelogram – ✔️ (given)
✔ Rectangle – ✔️ (given)
✔ Square – ✔️ (given)
✘ Trapezoid – No → ✘
✘ Isosceles Trapezoid – Diagonals are congruent but do not bisect each other → ✘
✔ Kite – One diagonal bisects the other, but not mutually → ✘ (unless it’s a rhombus/square)

> 💡 In a kite, only one diagonal is bisected by the other — they don’t bisect each other.

✔ So: Only Parallelogram, Rectangle, Square

---

Row 8: “Four sides congruent”

✔ Parallelogram – Not necessarily → ✘
✔ Rectangle – Not unless it’s a square → ✘
✔ Square – ✔️ (given)
✘ Trapezoid – ✘
✘ Isosceles Trapezoid – ✘
✔ Kite – Only if it’s a rhombus → ✘ (standard kite ≠ rhombus)

> 🧭 Note: A square is a special kite and rhombus, but a general kite does NOT have four congruent sides.

✔ Only Square

---

Row 9: “Four right angles”

✔ Parallelogram – Only if rectangle → ✘
✔ Rectangle – ✔️ (given)
✔ Square – ✔️ (given)
✘ Trapezoid – ✘
✘ Isosceles Trapezoid – ✘
✘ Kite – ✘ (unless it’s a square)

✔ Only Rectangle and Square

---

## ✔ Final Completed Table:

| 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 | ✘ | ✔️ | ✔️ | ✘ | ✘ | ✘ |

---

## 📝 Summary of Key Points:

- Parallelogram is the most basic — has opposite sides/angles equal, diagonals bisect.
- Rectangle adds 4 right angles and congruent diagonals.
- Square = Rectangle + Rhombus → all sides equal, all angles 90°, diagonals congruent & bisect.
- Trapezoid has only one pair of parallel sides — very few shared properties.
- Isosceles Trapezoid has congruent legs and congruent diagonals — unique!
- Kite has two pairs of adjacent congruent sides and one pair of opposite angles congruent.

---

✔ You now have the fully completed worksheet! Use this to study or grade your work. Let me know if you want a printable version or flashcards for these properties!