Question

Are all rectangles are squares are all parallelograms are rectangles

Answer 1

Let's clarify the relationships between rectangles, squares, and parallelograms:

1. **Parallelograms**: A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. The properties of a parallelogram include opposite angles being equal and the diagonals bisecting each other.

2. **Rectangles**: A rectangle is a specific type of parallelogram where all angles are right angles (90 degrees). Therefore, all rectangles are parallelograms.

3. **Squares**: A square is a specific type of rectangle (and a type of parallelogram) where all sides are of equal length and all angles are right angles. Therefore, all squares are rectangles.

So to summarize:
- All squares are rectangles (because they meet the criteria of having right angles and opposite sides equal in length).
- All rectangles are parallelograms (because they meet the criteria of having opposite sides parallel and equal).
- Not all parallelograms are rectangles (since a parallelogram can have angles that are not 90 degrees).
- Not all rectangles are squares (since a rectangle can have sides of different lengths).

In conclusion:
- **All squares are rectangles.**
- **All rectangles are parallelograms.**
- **Not all parallelograms are rectangles.**
- **Not all rectangles are squares.**