Incenter

The angle bisectors of the interior angles of a triangle are concurrent. Their point of intersection is called the Incenter. The incenter is the center of a circle that inscribes the triangle (click on the picture above for a larger view).

What do we know about the radius of the circle that inscribes the triangle?

Angle Bisectors

An angle bisector is a line that divides an angle into two equal parts.

If you draw two intersecting lines on a piece of paper, you should be able to draw the angle bisector between them. How do you do this?

What do we know about a point on the angle bisector relative to the sides of the angle?

Circumcenter

The perpendicular bisectors of the sides of a triangle are concurrent. Their point of intersection is called the circumcenter. The circumcenter is the center of a circle that circumscribes the triangle (click on the picture above for a larger view).

What do we know about the radius of the circle that circumscribes the triangle?

Perpendicular Bisector

The perpendicular bisector of a line segment AB is a line that is perpendicular to AB and passes through the midpoint of segment AB.

What to we know about the distance from any point on the perpendicular bisector to A and/or B?

Orthocenter

The altitudes of a triangle are concurrent (i.e. they meet at a single point). Their point of intersection is called the orthocenter.

The picture above shows the orthocenter of an acute triangle (click on the picture for a larger view). Where would the orthocenter be on an obtuse triangle? Where would it be on a right triangle?

Area of a Triangle

Area = (1/2)(base)(height)

Note: Two differently shaped triangles can have the same area. Why is this true?

Height of a Triangle

Height = Altitude (same thing)

The altitude is not always inside the triangle (e.g. an obtuse triangle).