Question

which statements are true? check all that apply. a square is sometimes a rhombus. a rectangle is sometimes a square. a parallelogram is sometimes a kite. a square is always a rhombus. a trapezoid is never a kite.

Explanation:

Step1: Analyze the relationship between square and rhombus

A square has all sides equal and all angles \(90^{\circ}\). A rhombus has all sides equal. Since a square satisfies the property of a rhombus (all sides equal), a square is always a rhombus. So the statement "A square is sometimes a rhombus" is false and "A square is always a rhombus" is true.

Step2: Analyze the relationship between rectangle and square

A rectangle has opposite sides equal and all angles \(90^{\circ}\). A square has all sides equal and all angles \(90^{\circ}\). When the adjacent sides of a rectangle are equal, it is a square. So a rectangle is sometimes a square.

Step3: Analyze the relationship between parallelogram and kite

A parallelogram has opposite sides equal and parallel. A kite has two pairs of adjacent sides equal. A parallelogram is not a kite (except in some degenerate cases which are not considered in standard definitions).

Step4: Analyze the relationship between trapezoid and kite

A trapezoid has one pair of parallel sides. A kite has two pairs of adjacent sides equal. A trapezoid cannot be a kite as their definitions and properties are distinct.

Answer:

B. A rectangle is sometimes a square.
D. A square is always a rhombus.
E. A trapezoid is never a kite.