Classifying
Quadrilaterals
“…geometric shapes are the
alphabet in which the book of
nature is written." -Galileo
Objectives
 Make distinct definitions of what
parallelograms, kites, rectangles,
squares, rhombi, and trapezoids are.
 Sort and classify quadrilaterals.
 Determine which shapes are and are
not quadrilaterals, given examples.
 Designate the best name for a given
quadrilateral, given examples.
 Construct a flow chart.
What is a Quadrilateral?
 A quadrilateral is a two-dimensional figure formed
by connecting four segments endpoint to endpoint
with each segment intersecting exactly two
others. It also has four sides and four angles.
What is a Quadrilateral?
 Look around you, do you
see shapes that could be
termed a quadrilateral?
 Take about two minutes
to draw five different
shapes that you think
could be classified as a
quadrilateral.
Types of Quadrilaterals
 Trapezoid
 Parallelogram
 Square
 Rectangle
 Kite, Dart
 Rhombus
 Rectangle
Classification of Quadrilaterals
 A concave
quadrilateral
contains at least one
angle that is >180o.
 A quadrilateral is
convex if each
vertex lies in the
interior of the
opposite angle.
Name that Quadrilateral!
 A square is a
quadrilateral with
all sides and
angles equal.
 If all quadrilaterals
have 360o total,
what is the angle
of each vertex in
a square?
Name that Quadrilateral!
 A quadrilateral with
all angles equal is a
rectangle.
 A quadrilateral with
all sides equal is a
rhombus.
Name that Quadrilateral!
 A quadrilateral with at least one pair of
parallel sides is a trapezoid.
Name that Quadrilateral!
 A quadrilateral with both
pairs of opposite sides
parallel and equal in
length is known as a
parallelogram.
 Parallelograms can be considered special cases
of trapezoids, since they have a least one pair
of parallel sides.
Name that Quadrilateral!
 A quadrilateral
with two separate
pairs of equal
adjacent sides is
commonly called
a kite.
 However, if the
kite is concave, a
dart is a more
appropriate term.
Are They Quadrilaterals?
A
B
C
 Examples of shapes or curves that are
not classified as quadrilaterals. They do
not follow the definition of a quadrilateral.
Can you give a reason why?
Put the Information to Use…
 Given the information in the preceding
slides, construct a flow chart of the
different shapes.
 You should begin with the definition of a
quadrilateral, and work your way down
the chart.
 A tree diagram would be the best
method for constructing the chart.