Question

understanding quadrilaterals
which statements are true? choose three correct answers.
a rectangle is sometimes a square.
a square is always a rhombus.
a trapezoid is never a kite.
a parallelogram is sometimes a kite.
a square is sometimes a rhombus.

Explanation:

Step1: Analyze the first statement

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

Step2: Analyze the second statement

A square has all sides equal and opposite sides parallel. A rhombus has all sides equal and opposite sides parallel. So, a square is always a rhombus.

Step3: Analyze the third statement

A trapezoid has one pair of parallel sides. A kite has two pairs of adjacent sides equal. These two definitions are mutually exclusive. So, a trapezoid is never a kite.

Step4: Analyze the fourth statement

A parallelogram has opposite sides equal and parallel. A kite has two pairs of adjacent sides equal. A parallelogram can only be a kite when it is a rhombus (a special case). But generally, a parallelogram is not a kite.

Step5: Analyze the fifth statement

Since a square has all the properties of a rhombus (all sides equal, opposite sides parallel), a square is always a rhombus, not sometimes.

Answer:

A rectangle is sometimes a square, A square is always a rhombus, A trapezoid is never a kite.