Book – a line, segment, or ray that intersects a... P.O.C. for the perpendicular bisectors is called the

Book – a line, segment, or ray that intersects a segment at
its midpoint forming a right angle.
Mr. Niven – Something that is perpendicular (forms a right
angle) to AND bisects (cut into two equal parts) a segment
(side of triangle)
P.O.C. for the perpendicular bisectors is called the
circumcenter. Can be inside, outside, or on triangle
The circumcenter is equidistant (same distance away) from
the 3 vertices of the triangle, therefore it is the center of
the circle with radius equal to the distance from the
circumcenter to any of the vertices. Making that the
circumscribed circle (which is a circle containing all the
vertices of a polygon)
Any point on a perpendicular bisector is equidistant from
the 2 endpoints (vertices) of the segment (triangle side) it
is bisecting.
Book – a ray that divides an angle into two congruent
adjacent angles
P.O.C. of the angle bisectors is called the incenter. Will
always be inside triangle.
Mr. Niven – a ray that cuts an angle into two smaller,
congruent angles that are right next to each other.
The Incenter is equidistant (the perpendicular distance)
from the 3 sides of the triangle, therefore it is the center of
the circle with radius equal to the distance from the
incenter to any of the sides. This is called the inscribed
circle.
A point that is on the angle bisector is equidistant from the
two sides of the angle (sides of triangle).
Book – a segment from a vertex of a triangle to the
midpoint of the opposite side of the triangle.
Mr. Niven – a segment connecting a vertex to the opposite
side’s midpoint
Book – The perpendicular segment from a vertex of a
triangle to the opposite side or to the line that contains the
opposite side.
P.O.C. is the Centroid. The Centroid is the center of gravity.
Always inside triangle
The Centroid cuts the medians into two parts. 1 part is
larger than the other. The smaller part is 1/3 of the whole
median and the larger part is 2/3 of the whole median.
The larger part of the median is twice as big as the smaller
part.
P.O.C. of the altitudes is called the orthocenter.
The orthocenter can be inside, outside or on the triangle.
The altitude must be perpendicular to the opposite side.
Mr. Niven – segment from a vertex to opposite side
forming a right angle.
Rotate the paper so that the altitude is the perpendicular
distance from the vertex to its opposite side. Altitude is the
height when that opposite side is the base.
Perpendicular Bisector
Angle Bisector
Median
Product of Mr. Niven
Altitude