Head First 2D Geometry

268 Chapter 6

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.

Square

Rhombus

Kite

Quadrilateral

A generic four-sided shape.

Two separate adjacent

pairs of congruent sides.

A rhombus has four

congruent sides, but no

right angles.

Four congruent sides,

all internal angles

are right angles.

This arrow means

that every kite is a

quadrilateral.

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.

A rhombus is both a type of kite and a type

of parallelogram. It has the prop ...