Quadrilaterals Graphic Organizer - Lindsay Bowden - Free Printable

This image is a "Quadrilaterals Checklist" worksheet. The task is to fill in the grid by marking which properties apply to each type of quadrilateral listed.

To solve this, I need to recall or research the geometric properties of each quadrilateral (Parallelogram, Rectangle, Rhombus, Square, Kite, Trapezoid, Isosceles Trapezoid) and check them against the properties listed in the columns (Opposite Sides Parallel, Opposite Sides Congruent, etc.).

I will go through each quadrilateral one by one, starting with the Parallelogram, and fill in the checklist based on its known properties.

Let's begin with the first row: Parallelogram.

- Opposite Sides Parallel: Yes, by definition.
- Opposite Sides Congruent: Yes, a property of parallelograms.
- Opposite Angles Congruent: Yes, another key property.
- All Equal Sides: No, only if it's a rhombus.
- All Equal Angles: No, only if it's a rectangle.
- Congruent Diagonals: No, diagonals are not necessarily congruent.
- Perpendicular Diagonals: No, not generally true.
- Diagonals Bisect Each Other: Yes, this is a defining property.

I will now move to the next row, Rectangle.

- Opposite Sides Parallel: Yes, it is a type of parallelogram.
- Opposite Sides Congruent: Yes, also a property of parallelograms.
- Opposite Angles Congruent: Yes, same reason.
- All Equal Sides: No, only if it’s a square.
- All Equal Angles: Yes, all angles are 90 degrees.
- Congruent Diagonals: Yes, diagonals of a rectangle are congruent.
- Perpendicular Diagonals: No, not generally true.
- Diagonals Bisect Each Other: Yes, since it’s a parallelogram.

Next, Rhombus.

- Opposite Sides Parallel: Yes, it is a parallelogram.
- Opposite Sides Congruent: Yes.
- Opposite Angles Congruent: Yes.
- All Equal Sides: Yes, that’s the definition of a rhombus.
- All Equal Angles: No, unless it’s a square.
- Congruent Diagonals: No, diagonals are not necessarily congruent.
- Perpendicular Diagonals: Yes, diagonals of a rhombus are perpendicular.
- Diagonals Bisect Each Other: Yes, as it’s a parallelogram.

Now, Square.

- Opposite Sides Parallel: Yes, it’s a parallelogram.
- Opposite Sides Congruent: Yes.
- Opposite Angles Congruent: Yes.
- All Equal Sides: Yes, it’s a rhombus.
- All Equal Angles: Yes, it’s a rectangle.
- Congruent Diagonals: Yes, it’s a rectangle.
- Perpendicular Diagonals: Yes, it’s a rhombus.
- Diagonals Bisect Each Other: Yes, it’s a parallelogram.

Next, Kite.

- Opposite Sides Parallel: No, generally not.
- Opposite Sides Congruent: No, adjacent sides are congruent, not opposite.
- Opposite Angles Congruent: No, only one pair of opposite angles may be congruent.
- All Equal Sides: No, only two pairs of adjacent sides are equal.
- All Equal Angles: No.
- Congruent Diagonals: No.
- Perpendicular Diagonals: Yes, diagonals are perpendicular.
- Diagonals Bisect Each Other: Only one diagonal is bisected by the other.

Now, Trapezoid (assuming general trapezoid, not isosceles).

- Opposite Sides Parallel: Yes, exactly one pair.
- Opposite Sides Congruent: No, not necessarily.
- Opposite Angles Congruent: No.
- All Equal Sides: No.
- All Equal Angles: No.
- Congruent Diagonals: No.
- Perpendicular Diagonals: No, not generally.
- Diagonals Bisect Each Other: No.

Finally, Isosceles Trapezoid.

- Opposite Sides Parallel: Yes, one pair.
- Opposite Sides Congruent: No, the non-parallel sides (legs) are congruent, but not opposite sides.
- Opposite Angles Congruent: No, base angles are congruent, but not opposite angles.
- All Equal Sides: No.
- All Equal Angles: No.
- Congruent Diagonals: Yes, diagonals are congruent in an isosceles trapezoid.
- Perpendicular Diagonals: No.
- Diagonals Bisect Each Other: No.

Based on this analysis, I can now provide the completed checklist.

Completed Quadrilaterals Checklist:

| Quadrilateral | Opposite Sides Parallel | Opposite Sides Congruent | Opposite Angles Congruent | All Equal Sides | All Equal Angles | Congruent Diagonals | Perpendicular Diagonals | Diagonals Bisect Each Other |
|---------------------|--------------------------|---------------------------|----------------------------|------------------|-------------------|------------------------|--------------------------|------------------------------|
| Parallelogram | ✔️ | ✔️ | ✔️ | ✘ | ✘ | ✘ | ✘ | ✔️ |
| Rectangle | ✔️ | ✔️ | ✔️ | ✘ | ✔️ | ✔️ | ✘ | ✔️ |
| Rhombus | ✔️ | ✔️ | ✔️ | ✔️ | ✘ | ✘ | ✔️ | ✔️ |
| Square | ✔️ | ✔️ | ✔️ | ✔️ | ✔️ | ✔️ | ✔️ | ✔️ |
| Kite | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✔️ | ✘ (only one diagonal bisected) |
| Trapezoid | ✔️ (one pair) | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ |
| Isosceles Trapezoid | ✔️ (one pair) | ✘ | ✘ | ✘ | ✘ | ✔️ | ✘ | ✘ |

Note: For the Kite, while diagonals do intersect and one is bisected, the phrase “Diagonals Bisect Each Other” typically means each diagonal cuts the other into two equal parts, which is not true for a kite. So, it’s marked as ✘.

This completes the solution.