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Triangles and centers all about

Triangles and centers all about

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.  



Intersect at the Orthocenter