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Honors Geometry Special Quadrilaterals

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True/False Every square is a rhombus.

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TRUE – four congruent sides

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True/False If the diagonals of a quadrilateral are perpendicular, then it is a rhombus.

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False – diagonals don’t have to be congruent or bisect each other.

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True/False The diagonals of a rectangle bisect its angles.

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FALSE (draw an EXTREME rectangle!)

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True/False A kite with all consecutive angles congruent must be a square.

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TRUE

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True/False Diagonals of trapezoids are congruent.

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FALSE – not always!

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True/False A parallelogram with congruent diagonals must be a rectangle.

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TRUE

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True/False Some rhombuses are rectangles.

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True – some rhombuses also have right angles

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True/False The diagonals of a rhombus are congruent.

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False – not always!

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True/False If the diagonals of a parallelogram are perpendicular, it must be a rhombus.

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TRUE

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True/False Diagonals of a parallelogram bisect the angles.

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FALSE

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True/False A quadrilateral that has diagonals that bisect and are perpendicular must be a square.

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FALSE (could be rhombus… right angles not guaranteed)

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Sometimes/Always/Never A kite with congruent diagonals is a square.

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FALSE – could be, but diagonals don’t have to bisect each other.

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Give the most descriptive name: A parallelogram with a right angle must be what kind of shape?

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Rectangle

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Give the most descriptive name: A rectangle with perpendicular diagonals must be what kind of shape?

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SQUARE

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Give the most descriptive name A rhombus with consecutive angles congruent must be a:

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SQUARE

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Give the most descriptive name: A parallelogram with diagonals that bisect its angles must be a:

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Rhombus

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Proving that a Quad is a Rectangle If a parallelogram contains at least one right angle, then it is a rectangle. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. If all four angles of a quadrilateral are right angles, then it is a rectangle.

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Proving that a Quad is a Kite If two disjoint pairs of consecutive sides of a quadrilateral are congruent, then it is a kite. If one of the diagonals of a quadrilateral is the perpendicular bisector of the other diagonal, then it is a kite.

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Proving that a Quad is a Rhombus If a parallelogram contains a pair of consecutive sides that are congruent, then it is a rhombus. If either diagonal of a parallelogram bisects two angles of the parallelogram, then it is a rhombus. If the diagonals of a quadrilateral are perpendicular bisectors of each other, then the quadrilateral is a rhombus.

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Proving that a Quad is a Square If a quadrilateral is both a rectangle and a rhombus, then it is a square.

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Proving that a Trapezoid is Isosceles If the non-parallel sides of a trapezoid are congruent, then it is isosceles. If the lower or upper base angles of a trapezoid are congruent, then it is isosceles. If the diagonals of a trapezoid are congruent, then it is isosceles.

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