Special quadrilaterals
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Special Quadrilaterals. Honors Geometry. 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.

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Special Quadrilaterals

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Special Quadrilaterals

Honors Geometry


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 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.


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.


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.


Proving that a Quad is a Square

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


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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