Special Quadrilaterals
Honors Geometry
Fill in all missing angle measures for
the RECTANGLE:
Fill in all missing angle measures for
the PARALLELOGRAM
Fill in the missing angle measures for
the RHOMBUS
Proving that a Quad is a Rectangle
 If a parallelogram _______________, then it is a rectangle.
 If a parallelogram _________________, then the
parallelogram is a rectangle.
 If a quadrilateral __________________, then it is a
rectangle.
Proving that a Quad is a Rectangle
 If a parallelogram contains at least one right angle, then it is a
rectangle.
 If a parallelogram has congruent diagonals, then the
parallelogram is a rectangle.
 If a quadrilateral has four right angles, then it is a rectangle.
Proving that a Quad is a Kite
 If a quadrilateral ________________________, then it is
a kite.
 If a quadrilateral ________________________, then it is
a kite.
Proving that a Quad is a Kite
 If a quadrilateral has two disjoint pairs of consecutive sides
congruent, then it is a kite.
 If a quadrilateral has one diagonal that is a perpendicular
bisector of the other, then it is a kite.
Proving that a Quad is a Rhombus
 If a parallelogram ______________________, then it is a
rhombus.
 If a parallelogram _______________________, then it is
a rhombus.
 If a quadrilateral _________________________, then the
quadrilateral is a rhombus.
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 a parallelogram has either diagonal bisecting opposite
angles, then it is a rhombus.
 If a quadrilateral has diagonals that are perpendicular
bisectors of each other, then the quadrilateral is a rhombus.
Proving that a Quad is a Square
 If a quadrilateral ______________________, then it is a
square.
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 a trapezoid _________________________, then it is
isosceles.
 If a trapezoid _________________________, then it is
isosceles.
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.
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 each other and are perpendicular
must be a square.
FALSE (could be rhombus…
diagonals not guaranteed to be
congruent)
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
Geometry in 3D!!!
If parallel lines lie in two distinct
planes, the planes must be parallel.
FALSE
Three planes can intersect at a point.
TRUE (ex: corner of
classroom)
Three planes can intersect at a line.
TRUE
If two lines in space are not
parallel, then they must intersect.
FALSE (Skew lines)
If lines are perpendicular to the
same plane, they are parallel.
TRUE
If a line is perpendicular to a line in
a plane, then it is perpendicular to
the plane.
FALSE (Mailbox
problem… must be perp.
to two lines in plane
passing through foot)
If a line is perpendicular to one of
two parallel planes, then it is
perpendicular to the other.
TRUE
If a line is perpendicular to a plane,
then it is perpendicular to all lines
in the plane.
FALSE (Not perp. to
lines not passing through
its foot)
If separate planes contain skew lines,
the planes are parallel.
FALSE
Two planes can intersect at a point.
FALSE (planes continue
infinitely)
Two planes can intersect at a line.
TRUE (crack at top of
classroom)
Two intersecting lines can lie in more
than one plane.
FALSE (intersecting
lines determine a plane)
Two parallel lines determine a plane.
TRUE
Two skew lines determine a plane.
FALSE (by definition,
skew lines lie in different
planes)
Three points determine a plane.
FALSE (must be noncollinear)
If three lines are parallel, then they must
be coplanar.
FALSE
In a plane, if two lines are
perpendicular to the same line, they
are parallel.
TRUE
In space, if two lines are perpendicular to
the same line, they are parallel.
FALSE