CH 3 Centers of Triangles Notes
Name of special
segment / ray / line
Midsegment
Perpendicular
bisector
Angle bisector
Median
Altitude
Definition / Description
Special properties
of the segment /
ray / line.
A midsegment of a triangle
is a segment connecting
midpoints of two sides of a
triangle.
A midsegment is
parallel to and half
the length of the
opposite side of
the triangle.
A perpendicular bisector of
a segment is a line that is
perpendicular to the
segment at its midpoint.
Any point on the
perpendicular
bisector is
equidistant from
the endpoints of
the segment.
An angle bisector is a ray
that divides an angle into
two congruent angles.
A median of a triangle is a
segment whose endpoints
are a vertex and the
midpoint of the opposite
side.
An altitude of a triangle is
the perpendicular segment
from a vertex of a triangle
to the line containing the
opposite side.
Picture…
Are all three concurrent in a
triangle? If so, what is the name
of the point of concurrency?
Special properties of the point of
concurrency.
No.
N/A
1) The circumcenter is equidistant
from each vertex of the triangle.
Yes – circumcenter.
Any point on the
angle bisector is
equidistant from
the sides of the
angle (measured
at 90-degrees).
Yes –
incenter
.
2) The circumcenter is the center of a
circle that can be circumscribed so
that it passes through each vertex of
the triangle.
1) The incenter is equidistant from
each side of the triangle (measured at
90-degrees).
2) The incenter is the center of a
circle that can be inscribed so that it
just touches each side of the triangle.
1) The centroid divides each median
into 2/3 and 1/3 portions.
2) The centroid is the center of gravity
of the triangle.
Yes – centroid.
Yes –
orthoc
enter.
None.