quad relationships
The quadrilateral family tree
There’s one key thing that the shapes in this chapter all have in
common—they all have four sides.
Any shape that has four straight sides is a quadrilateral.
Parallelograms, kites, and trapezoids are all part of the
quadrilateral family, along with shapes such as squares and
rectangles. Here’s the quadrilateral family tree so you
can see how they’re all related.
The arrows show you the
hierarchy
The thick arrows on the family
tree show you the relationships
between the shapes. Any shape
at the end of an arrow is a more
specialized form of the shape that
the arrow is coming from. So a
kite is a type of quadrilateral since
it shares the same properties as
a quadrilateral—it has four sides,
with two pairs of separate adjacent
sides. Similarly, a square is type of
rhombus, which means it is also a
type of kite.
The family tree also shows you
which shapes are not directly related.
That means a kite is not a type of
parallelogram and a rectangle is
not a type of trapezoid.
Square
Rhombus
Kite
Quadrilateral
A
generic
four-sided
shap
e.
T
w
o separa
te adjac
ent
pair
s of congruent sides.
A rhombus has f
our
congruent sides, but no
r
ight angles.
Four congruent sides,
all interna
l angles
ar
e right angles.
T
his arrow means
tha
t ev
ery ki
te is a
quadr
il
atera
l.
A rhombus is both a typ
e of kite and a typ
e
of para
llelogram. It has the prop
erties of
both.
268 Chapter 6
Square
T
w
o pair
s of para
llel
sides. They are
congruent, t
oo.
and a separa
te pair of
congruent sides with
congruent angles.
T
w
o pair
s of para
llel
congruent sides and
a
ll interna
l angles
are right angles.
If ther
e’s one pair of
para
llel sides it’s a trap
ezoid,
if ther
e ar
e t
wo pair
s of
para
llel sides, then i
t’s a
para
llelogram.
quadrilaterals
Isosceles
Trapezoid
Trapezoid
Exac
tl
y one pair of para
llel sides
Rectangle
Parallelogram
One pair of para
llel sides,
you are here 4 269
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