The true statement among those listed is:
**All parallelograms are quadrilaterals.**
Let's break down why the other statements are not true:
1. **All parallelograms are rectangles.**
- This is false because while all rectangles are parallelograms (parallelograms with right angles), not all parallelograms have right angles. A general parallelogram has two pairs of parallel sides but does not necessarily have four right angles.
2. **All quadrilaterals are parallelograms.**
- This is false because a quadrilateral is any four-sided figure, whereas a parallelogram is a specific type of quadrilateral with both pairs of opposite sides parallel. For example, a trapezoid is a quadrilateral but not a parallelogram.
3. **All rectangles are squares.**
- This is false because rectangles are defined as having opposite sides equal and all angles right angles, but squares are a more specific type of rectangle in which all four sides are of equal length. Not all rectangles have four sides of equal length.
Therefore, the only correct statement is: **All parallelograms are quadrilaterals.**
Which statement is true?
All parallelograms are rectangles.
All parallelograms are quadrilaterals.
All quadrilaterals are parallelograms.
All rectangles are squares.
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1 answer