Question

true false a rectangle is a square. a square is a rectangle. a rhombus is a square. a square is a rhombus. a square is a kite. a kite is a square. a parallelogram is a rhombus. a rhombus is a parallelogram. a trapezoid is a quadrilateral. a quadrilateral is a trapezoid.

Explanation:

Step1: Recall definitions

• Quadrilateral: 4 - sided polygon.
• Trapezoid: Quadrilateral with at least one pair of parallel sides (or exactly one, depending on definition).
• Rectangle: Quadrilateral with 4 right angles, opposite sides equal.
• Square: Rectangle with all sides equal (so 4 right angles, all sides equal).
• Rhombus: Quadrilateral with all sides equal, opposite sides parallel, opposite angles equal.
• Kite: Quadrilateral with two distinct pairs of adjacent sides equal.
• Parallelogram: Quadrilateral with both pairs of opposite sides parallel and equal.

Step2: Evaluate each statement

1. A rectangle is a square: A rectangle has 4 right angles, but sides can be unequal. A square needs all sides equal. So False.
2. A square is a rectangle: A square has 4 right angles and all sides equal (so opposite sides equal). Satisfies rectangle definition. True.
3. A rhombus is a square: A rhombus has all sides equal but angles may not be right. A square needs right angles. So False (unless rhombus has right angles, but not all rhombuses do).
4. A square is a rhombus: A square has all sides equal, opposite sides parallel, opposite angles equal. Satisfies rhombus definition. True.
5. A square is a kite: A square has two distinct pairs of adjacent sides equal (all sides equal, so adjacent sides equal). Satisfies kite definition (two distinct pairs of adjacent sides equal). True.
6. A kite is a square: A kite has two distinct pairs of adjacent sides equal, but angles may not be right, sides may not be all equal. So False (unless kite has right angles and all sides equal, but not all kites do).
7. A parallelogram is a rhombus: A parallelogram has opposite sides equal, but not necessarily all sides equal. A rhombus needs all sides equal. So False.
8. A rhombus is a parallelogram: A rhombus has both pairs of opposite sides parallel and equal (all sides equal, so opposite sides equal). Satisfies parallelogram definition. True.
9. A trapezoid is a quadrilateral: A trapezoid has 4 sides, so it's a quadrilateral. True.
10. A quadrilateral is a trapezoid: A quadrilateral is a 4 - sided polygon. A trapezoid needs at least one pair of parallel sides. Not all quadrilaterals have parallel sides (e.g., a kite with no parallel sides). So False.

Answer:

1. A rectangle is a square: False
2. A square is a rectangle: True
3. A rhombus is a square: False
4. A square is a rhombus: True
5. A square is a kite: True
6. A kite is a square: False
7. A parallelogram is a rhombus: False
8. A rhombus is a parallelogram: True
9. A trapezoid is a quadrilateral: True
10. A quadrilateral is a trapezoid: False