Question

Put an X in the box if the shape always has the property. 1. Both pairs of opp. sides are 2. Diagonals are 3. Diagonals are er endicular 4. Diagonals bisect each other 5. Consecutive angles are su lementa 6. Both pairs of opposite L's are:
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
Isosceles
Kite
Trapezoid

Answer 1

Let's evaluate each shape based on the properties you listed. Here are the properties marked for each shape:

| Shape | Opposite sides are parallel | Diagonals are equal | Diagonals are perpendicular | Diagonals bisect each other | Consecutive angles are supplementary | Both pairs of opposite angles are equal |
|--------------|-----------------------------|---------------------|-----------------------------|-----------------------------|------------------------------------|-------------------------------------|
| Parallelogram| X | | | X | X | X |
| Rectangle | X | X | | X | X | X |
| Rhombus | X | | X | X | X | X |
| Square | X | X | X | X | X | X |
| Trapezoid | X (only for some types) | | | | X (only for some types) | |
| Isosceles Trapezoid| X | | | | X | |
| Kite | | | X | | X | |

### Summary of Properties:
1. **Both pairs of opposite sides are parallel**:
- **Parallelogram**: X
- **Rectangle**: X
- **Rhombus**: X
- **Square**: X
- **Trapezoid**: Only for some types (not always)
- **Isosceles Trapezoid**: X (only for some types)
- **Kite**: Not applicable.

2. **Diagonals are equal**:
- **Rectangle**: X
- **Square**: X
- **Parallelogram**: Not applicable.
- **Rhombus**: Not applicable.
- **Trapezoid**: Not applicable.
- **Isosceles Trapezoid**: Not applicable.
- **Kite**: Not applicable.

3. **Diagonals are perpendicular**:
- **Rhombus**: X
- **Square**: X
- **Kite**: X
- **Parallelogram**: Not applicable.
- **Rectangle**: Not applicable.
- **Trapezoid**: Not applicable.
- **Isosceles Trapezoid**: Not applicable.

4. **Diagonals bisect each other**:
- **Parallelogram**: X
- **Rectangle**: X
- **Rhombus**: X
- **Square**: X
- **Trapezoid**: Not applicable.
- **Isosceles Trapezoid**: Not applicable.
- **Kite**: Not applicable.

5. **Consecutive angles are supplementary**:
- **All shapes shown would have this property**.

6. **Both pairs of opposite angles are equal**:
- **Parallelogram**: X
- **Rectangle**: X
- **Rhombus**: X
- **Square**: X

### Conclusion:
The only shapes that consistently fulfill all properties listed are Parallelograms, Rectangles, Rhombuses, and Squares. Trapezoids, Isosceles Trapezoids, and Kites do not uniformly meet all the properties.