e or false 11. Every trapezoid is a quadrilateral. 12. Every square is a rhombus 13. Every rhombus is a parallelogram 14. Every rectangle is a rhombus 15. A square is both a rectangle & a rhombus.
The Correct Answer and Explanation is:
Here are the true or false answers along with explanations:
- Every trapezoid is a quadrilateral.
True. A trapezoid is defined as a four-sided figure with at least one pair of parallel sides. Since it has four sides, it is a type of quadrilateral. - Every square is a rhombus.
True. A square is a special type of rhombus where all angles are 90 degrees. A rhombus is a quadrilateral where all sides have equal length, and a square satisfies this property. - Every rhombus is a parallelogram.
True. A rhombus is a quadrilateral with all sides of equal length. Since opposite sides of any rhombus are parallel, it is also a parallelogram (which is defined as a quadrilateral with opposite sides parallel). - Every rectangle is a rhombus.
False. While both rectangles and rhombuses are parallelograms, a rectangle has four right angles, and the sides don’t necessarily have to be of equal length. A rhombus requires all sides to be of equal length, which is not a requirement for a rectangle. - A square is both a rectangle & a rhombus.
True. A square has all the properties of both a rectangle and a rhombus. It is a rectangle because it has four right angles, and it is a rhombus because all its sides have equal length. Therefore, a square is a special case of both shapes.
These geometric properties help us classify quadrilaterals into different categories, showing how some figures can fit into multiple categories based on their characteristics.
