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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