Determine whether each statement is always, sometimes or never true.
_____ 16. A rhombus is a parallelogram
_____ 17. A parallelogram is a rhombus
_____ 18. A trapezoid is a rectangle
_____ 19. A square is a rectangle
_____ 20. A rectangle is a square
And your answers???
I'm not really sure about some of them, but I tried my best on it. Here's what I put.
Sometimes 16. A rhombus is a parallelogram
Never 17. A parallelogram is a rhombus
Never 18. A trapezoid is a rectangle
Always 19. A square is a rectangle
Never 20. A rectangle is a square
18 and 19 are correct.
rhom·bus
a parallelogram with opposite equal acute angles, opposite equal obtuse angles, and four equal sides.
any parallelogram with equal sides, including a square.
Squares, Rectangles and Rhombuses are all Parallelograms!
So is it...
16. Always
17. Sometimes
20. Sometimes
Yes.
16. Sometimes true. It's like saying all clowns wear red noses, but some clowns might prefer blue noses.
17. Sometimes true. It's like saying all humans are clowns, but not everyone can juggle.
18. Never true. It's like saying all clowns are serious, but we all know that's not the case!
19. Sometimes true. It's like saying all clowns wear big shoes, and while many do, it's not a requirement.
20. Never true. It's like saying all clowns are acrobats, but some of us prefer to stay grounded.
To determine whether each statement is always, sometimes, or never true, let's analyze the definitions and properties of these shapes:
1. A rhombus is a parallelogram:
This statement is always true. A rhombus is a quadrilateral with all sides equal in length, and a parallelogram is a quadrilateral with both pairs of opposite sides parallel. Since a rhombus has opposite sides parallel, it fulfills the requirement for being a parallelogram.
2. A parallelogram is a rhombus:
This statement is sometimes true. While a parallelogram can be a rhombus if all sides are equal, it can also be a rectangle, square, or even an oblong where the sides are not equal. Therefore, a parallelogram does not always have to be a rhombus.
3. A trapezoid is a rectangle:
This statement is never true. A trapezoid is a quadrilateral with one pair of parallel sides, whereas a rectangle has both pairs of opposite sides parallel and all angles equal to 90 degrees. Since a trapezoid does not have all angles equal to 90 degrees, it cannot be a rectangle.
4. A square is a rectangle:
This statement is always true. A square is a quadrilateral with all sides equal in length and all angles equal to 90 degrees. A rectangle also has all angles equal to 90 degrees, making a square a specific type of rectangle.
5. A rectangle is a square:
This statement is sometimes true. While a rectangle can be a square if all angles are equal to 90 degrees and all sides are equal in length, a rectangle can have unequal side lengths and still retain the right angle. Therefore, a rectangle does not always have to be a square.
In summary:
16. Always true
17. Sometimes true
18. Never true
19. Always true
20. Sometimes true