special quadrilaterals

Honors Geometry

Special Quadrilaterals

True/False

Every square is a rhombus.

TRUE – four congruent sides

True/False

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

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

True/False

The diagonals of a rectangle bisect its angles.

FALSE (draw an EXTREME rectangle!)

True/False

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

TRUE

True/False

Diagonals of trapezoids are congruent.

FALSE – not always!

True/False

A parallelogram with congruent diagonals must be a rectangle.

TRUE

True/False

Some rhombuses are rectangles.

True – some rhombuses also have right angles

True/False

The diagonals of a rhombus are congruent.

False – not always!

True/False

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

TRUE

True/False

Diagonals of a parallelogram bisect the angles.

FALSE

True/False

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

FALSE (could be rhombus… right angles not guaranteed)

Sometimes/Always/Never

A kite with congruent diagonals is a square.

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

Give the most descriptive name:

A parallelogram with a right angle must be what kind of shape?

Rectangle

Give the most descriptive name:

A rectangle with perpendicular diagonals must be what kind of shape?

SQUARE

Give the most descriptive name

A rhombus with consecutive angles congruent must be a:

SQUARE

Give the most descriptive name:

A parallelogram with diagonals that bisect its angles must be a:

Rhombus

Proving that a Quad is a RectangleIf 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.

Proving that a Quad is a KiteIf 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.

Proving that a Quad is a RhombusIf 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.

Proving that a Quad is a SquareIf a quadrilateral is both a rectangle and a

rhombus, then it is a square.

Proving that a Trapezoid is IsoscelesIf 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.