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Never

A trapezoid is a parallelogram.

Always

The diagonals of a rectangle bisect eachother.

Sometimes

An equilateral parallelogram is equiangular.

Sometimes

The diagonals of a rhombus are equal.

Never

There is one right angle in a parallelogram and it is not a rectangle.

Always

An equiangular rhombus is a square.

Sometimes

The opposite angles of a parallelogram are supplementary.

Sometimes

The diagonals of a rectangle are the bisectors of the angles.

Always

A square is a rectangle.

Never

A trapezoid is a parallelogram.

Sometimes

A rhombus is a square.

Sometimes

The diagonals of a quadrilateral are perpendicular and the quadrilateral is not a rhombus.

Always

The diagonals of a rectangle bisect eachother.

Never

The diagonals of a kite are the perpendicular bisectors of each other.

Sometimes

The diagonals of a trapezoid are perpendicular.

Sometimes

An equilateral parallelogram is equiangular.

Sometimes

The angles of a parallelogram are congruent.

Never

A kite is a square.

Sometimes

The diagonals of a rhombus are equal.

Sometimes

An equilateral quadrilateral is a square.

Never

There are more than two right angles in a trapezoid.

Sometimes

If a quadrilateral has three angles of equal measure, then the fourth angle must be a right angle.

Always

The diagonals of an isosceles trapezoid are congrent.