Question

Problem 7D
What do these shapes have in common?
A shape with four sides. The adjacent sides are of unequal length. The shape has two sets of parallel sides and has four right angles.
A shape with four sides of equal length. The shape has two sets of parallel sides and has four right angles.
A shape with four sides of equal length. The shape has two sets of parallel sides and has four right angles.
Choose all answers that apply:
Choose all answers that apply:
(Choice A) They are all quadrilaterals.
A
They are all quadrilaterals.
(Choice B) They are all rectangles.
B
They are all rectangles.
(Choice C) They are all squares.
C
They are all squares.
(Choice D) None of the above
D
None of the above

Answer 1

To analyze the three described shapes:

1. **First Shape**: A shape with four sides, adjacent sides of unequal length, two sets of parallel sides, and four right angles. This shape is a **rectangle** but not a square.

2. **Second Shape**: A shape with four sides of equal length, two sets of parallel sides, and four right angles. This shape is a **square** but is also a rectangle.

3. **Third Shape**: Identical to the second shape, it is also a **square** and, therefore, a rectangle as well.

Now, let's evaluate the choices:

- **(Choice A)**: They are all quadrilaterals.
**True**. All three shapes are quadrilaterals since they have four sides.

- **(Choice B)**: They are all rectangles.
**False**. The first shape is a rectangle, but the second and third shapes are squares, which are a type of rectangle.

- **(Choice C)**: They are all squares.
**False**. The first shape is not a square.

- **(Choice D)**: None of the above.
**False**. We established in (Choice A) that they are all quadrilaterals.

**Conclusion**: The only correct choice is:
- (Choice A) They are all quadrilaterals.