Head First 2D Geometry

182 Chapter 4

triangle centers

A triangle has more than one center

Believe it or not, there are four common ways of finding the “center” of a triangle.

All three

intersect at the

centroid.

These lines are called

MEDIANS—they chop the

area of the triangle in two.

1

2

3

CENTROID

ORTHOCENTER

INCENTER

A

BC

Midpoint

of AB

Midpoint of AC

Midpoint of BC

A

BC

Altitude

on AB

Draw a circle inside which

just touches all three sides.

Incenter is center of the “incircle.”

“incircle”

The incenter is the center of the

biggest circle you can draw inside

the triangle.

The orthocenter is the intersection

of the altitudes drawn on all three

sides.

The centroid is the intersection of all

three medians (lines from the midpoint

of a side to the opposite vertex).

Altitudes go from a vertex to

meet the opposite side, and

are perpendicular to that side.

Altitude on BC

Altitude on AC

A line from the incenter

to a vertex exactly bisects

the angle at that vertex.

you are here 4 183

triangle properties

Circle drawn outside

through all three

vertices.

Centroid

“The point nearest to all

three fences”

Which kind of center was each of your buddies describing?

Pair ’em up! (You’ll have one center left over.)

Orthocenter

“The point nearest to all

three corners”

“The point where half the

crowd is on either side, no

matter which way you ...