Points of Concurrency Mini Unit

Perpendicular Bisectors

Points intersect at the circumcenter of a triangle

The circumcenter is _____ from each vertex

Equidistant

If the lines from the vertexes to the point in a triangle are congruent:

Perpendicular bisectors

Where is the circumcenter in an obtuse triangle

Outside the diagram

Where is the circumcenter in a right triangle

on the hypotenuse — midpoint of the hypotenuse

Where is the circumcenter in an acute triangle

in the diagram

Medians

Points intersect at the centroid/center of gravity

The centroid is located ____ of the distance of the median to the vertex

2/3

Can the centroid be located outside the triangle

No - always inside

Angle bisectors

Points intersect at the incenter

Incenters are ____ to each side of the triangle

equidistant

If the perpendicular distances from the points to each side are congruent…

Angle bisectors

Altitudes

Points intersect at the orthocenter

Can be orthocenter be located outside the triangle?

Yes - Obtuse triangles

When is a point the incenter, circumcenter and orthocenter?

When it’s equilateral triangle

What is another way to find the coordinates of a centroid?

Average all the points