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# Triangles and centers all about

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Author: c o
##### Description:

To learn definitions and see examples the various line segments and points within a triangle, including the centroid, the incenter, the orthocenter, circumcenter, the altitude, and the median.

Introduces each objective term in turn and displays an example.

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Tutorial

## Background

Before starting this lesson you should be familiar with the following terms and concepts, which we will quickly review here.

### Bisection

Lines segments and angles can both be bisected.  This means a line is made to intersect them such that they are divided intot two equal parts.

### Perpendicular

Two lines are perpendicular if the angle of their intersection is 90 degrees.

### Congruent

Two triangles are congruent if they have the same size.  That is, if you can place on on top of the other such that they overlap perfectly.

## The Centroid

### Medians of a Triangle

The medians of a triangle are the three line segments that join the three vertices with the midpoints of the sides opposite them.  E.g.

### Centroid

The three medians intersect at a point within the triangle called the centroid.

## The Circumcenter

### Perpendicular bisectors

A perpendicular bisector of a triangle is a line that bisects one of the sides, intersecting it at 90 degrees.

### Intersect at the circumcenter

The perpedicular bisectors intersect at a point called the circumcenter.  The circumcenter may be located on the inside or the outside of the triangle.

## Incenter

### Angle Bisector

A line that bisects one of the angles at the vertices of a triangle is an angle bisector of that triangle.

### Intersect at the Incenter

Unlike the circumcenter, the incenter is always found within the triangle.

## The Orthocenter

### The altitudes of a triangle

An altitude of a triangle is a perpendicular line drawn from one of its sides to the vertex opposite it.