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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.