Question

determine whether the following statements are true or false:

1. all squares are rectangles
false
2. all squares are parallelograms
false
3. all rectangles are parallelograms
true
4. all squares are rhombuses
true
5. all rhombuses are parallelograms
true

Answer 1

All statements are true.

A rectangle simply requires that a four-edged figure has 4 right angles and two sets of parallel lines. A square is a special case-- that all four sides are the same length, but it's still a rectangle.

The rest of your answers are correct. :-)

It then follows that if all squares are rectangles and all rectangles are parallelograms, that all squares are parallelograms. (This is modus ponens, more commonly known as the (hypothetical) syllogism. You don't need to know this, but it's an interesting topic... to me anyway, lol.)

Answer 2

thanks! i have another one:
fill in the blanks with sometimes, always, or never.
A square is always a rectangle.
A square is sometimes a rhombus.
A rhombus is sometimes a square.
A parallelogram is never a trapezoid.
A trapezoid is never a kite.
A rhombus is never a rectangle