# Assignment 4: Concurrencies of a Triangle

## Relative Locations of Triangle Centers

A Centroid is formed in a triangle by the intersection of segments from the MIDPOINT of the SIDES to the OPPOSITE VERTEX, like this:

Think about how the Centroid is constructed.

Do you think the Centroid is always on the Interior of the Triangle?
How can you test your thoughts?

Take a look at an animated version of a Triangle with its Centroid.

# Centroid Animation

Can you explain why the Position of the Centroid behaves the way it does as we change the Triangle?

An Orthocenter is formed in a triangle by the intersection of the ALTITUDES:

We can construct the Orthocenter by making lines Perpendicular from each side to the Opposite vertex, like this:

Do you think the Orthocenter is always inside the Triangle?

# Orthocenter Animation

Why does the Othocenter move the way it does?
(It may help to consider how the Orthocenter is constructed.)

### Do you think the Circumcenter can ever lie on the Exterior of the Triangle?

Take a look at the animation.

# Circumcenter Animation

Did the Circumcenter behave the way you expected it to?

Can you explain why it behaves the it does?