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Special Quadrilaterals

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Special Quadrilaterals

Honors Geometry

Every square is a rhombus.

TRUE – four congruent sides

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.

The diagonals of a rectangle bisect its angles.

FALSE (draw an EXTREME rectangle!)

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

TRUE

Diagonals of trapezoids are congruent.

FALSE – not always!

A parallelogram with congruent diagonals must be a rectangle.

TRUE

Some rhombuses are rectangles.

True – some rhombuses also have right angles

The diagonals of a rhombus are congruent.

False – not always!

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

TRUE

Diagonals of a parallelogram bisect the angles.

FALSE

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

FALSE (could be rhombus… right angles not guaranteed)

A kite with congruent diagonals is a square.

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

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

Rectangle

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

SQUARE

A rhombus with consecutive angles congruent must be a:

SQUARE

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

Rhombus

- 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.

- 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.

- 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.

- If a quadrilateral is both a rectangle and a rhombus, then it is a square.

- 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.