circumcenter triangles

circumcenter

the point where all perpendicular bisectors intersect that is equidistant from the vertices, circle outside touching all vertices

incenter

point where all angle bisectors of a triangle intersect that is equidistant from the sides, circle inside

median

a segment joining a vertex to the midpoint of the opposite side

centroid

the point where all three medians intersect

special properties for centroid

for median AE and centroid P; AP=2/3AE & PE =1/3AE and 2PE=AP & ½AP=PE

altitude

a segment joining a vertex to the opposite side so that it is perpendicular to that side

orthocenter

the point where all three altitudes of a triangle intersect

point of concurrency

the point where concurrent lines intersect

concurrent lines

3 or more lines that intersect at a common point

how to find circumcenter

1. find midpoint of each side

2. find slope of each side

3. make slopes perpendicular

4. draw or solve system of equations

   -for system of equations use midpoint to find y intercept

how to find orthocenter

1. find slope of each side

2. find slope of each altitude (perpendicular slope)

3. draw out graph or use point that line goes through and use system of equations

how to find centroid

1. find midpoint of each side

2. draw median by connecting to opposite point or use point/midpoint + perpendicular slope to find the equation of median

3. solve system of equations