PLS ANSWER ASAP Determine whether the following statement is sometimes true, always true, or never true.
All rectangles are parallelograms.
A) Never true
B) Sometimes true *****
C) Always true
The statement "All rectangles are parallelograms" is sometimes true.
Explanation:
A rectangle is defined as a quadrilateral with all angles equal to 90 degrees. A parallelogram is a quadrilateral with opposite sides parallel.
Since all rectangles have opposite sides that are parallel (which is a defining characteristic of parallelograms), the statement is sometimes true. However, not all parallelograms have all angles equal to 90 degrees, so there are parallelograms that are not rectangles. Hence, the statement is not always true.
Therefore, the correct answer is B) Sometimes true.
To determine whether the statement "All rectangles are parallelograms" is sometimes true, always true, or never true, let's consider the definitions of both rectangles and parallelograms.
1. Rectangle: A rectangle is a quadrilateral with four right angles.
2. Parallelogram: A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length.
Now, to decide whether the statement is true, we need to analyze the relationship between rectangles and parallelograms.
A rectangle can always be considered a parallelogram because a rectangle meets the criteria of a parallelogram: it has opposite sides that are parallel. Additionally, a rectangle's opposite sides are equal in length, which is a requirement for a parallelogram as well. Therefore, whenever you have a rectangle, you can say that it is a parallelogram. This means the statement is always true.
Hence, the correct answer is C) Always true.