5.3 Concurrent Lines, Medians, and Altitudes
Can you figure out the puzzle below???
Stand Stand
0_23456789
No one understands!
Definitions
Concurrent Lines: Three or more lines that meet at one point.
Point of Concurrency: The point at which concurrent lines meet.
l
P
m
k
n
Properties of Bisectors
Circumcenter of the Triangle: The point of concurrency of the
perpendicular bisectors of a triangle.
Theorem 5-6: The perpendicular bisectors of the sides of a triangle
are concurrent at a point equidistant from the vertices.
Properties of Bisectors
Incenter of the Triangle: The point of concurrency of the angle
bisectors of a triangle.
Theorem 5-7: The bisectors of the angles of a triangle are concurrent
at a point equidistant from the sides.
Definitions
Median of a Triangle: A segments whose endpoints are a vertex and
the midpoint of the opposite side.
Altitude of a Triangle: Perpendicular segment from a vertex to the
line containing the opposite side.
Properties of Medians
Centroid of a Triangle: The point of concurrency of the medians of
a triangle.
Theorem 5-8: The medians of a triangle are concurrent at a point that
is two thirds the distance from each vertex to the midpoint of the
opposite sides.
2
2
2
DC 
3
DJ
EC 
3
EG
FC 
3
FH
Properties of Medians
In the figure below, DE = 6 and AD = 16. Find DB and AF.
F
Properties of Altitudes
Orthocenter of a Triangle: The point of concurrency of the lines
containing the altitudes of a triangle.
Theorem 5-9: The lines that contain the altitudes of a triangle are
concurrent.
Sum It Up

Figure
concurrent at..
which is…
bisector
circumcenter
equidistant from vertices
 bisector
incenter
equidistant from sides
median
centroid
2/3 distance from vertices
to midpoint
altitude
orthocenter
---------------------
5.3 Concurrent Lines, Medians, and Altitudes
Can you figure out the puzzle below???
KNEE
LIGHT LIGHT
HW 5.3: #8-9, 11-16, 19-22, 28
Neon Lights