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###
Never

A trapezoid is a parallelogram.

###
Always

The diagonals of a rectangle bisect eachother.

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Sometimes

An equilateral parallelogram is equiangular.

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Sometimes

The diagonals of a rhombus are equal.

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Never

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

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Always

An equiangular rhombus is a square.

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Sometimes

The opposite angles of a parallelogram are supplementary.

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Sometimes

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

###
Always

A square is a rectangle.

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Never

A trapezoid is a parallelogram.

###
Sometimes

A rhombus is a square.

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Sometimes

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

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Always

The diagonals of a rectangle bisect eachother.

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Never

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

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Sometimes

The diagonals of a trapezoid are perpendicular.

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Sometimes

An equilateral parallelogram is equiangular.

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Sometimes

The angles of a parallelogram are congruent.

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Never

A kite is a square.

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Sometimes

The diagonals of a rhombus are equal.

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Sometimes

An equilateral quadrilateral is a square.

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Never

There are more than two right angles in a trapezoid.

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Sometimes

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

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Always

The diagonals of an isosceles trapezoid are congrent.

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