Download Special Segments and Points of Concurrency in Triangles Key

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Honors Geometry
Organizer: Lessons 5-2 and 5-3
Special Segments and Points of Concurrency in Triangles
Perpendicular
Bisectors
Medians
B
Sketch Segments
Mark Known Information
(Congruences and Right
Angles)
Name of the
Point of Concurrency
(POC)
Location of POC*
Acute Triangle
Obtuse Triangle
Right Triangle
E
E
Centroid
F
C
A
Angle Bisectors
B
B
D
A
Altitudes
E
F
G D
F
B
D
G
C
A
D
C
C
A
CENTROID
CIRCUMCENTER
ORTHOCENTER
INCENTER
INSIDE
INSIDE
INSIDE
INSIDE
INSIDE
OUTSIDE
OUTSIDE
INSIDE
INSIDE
MIDPOINT OF THE
HYPOTENUSE
VERTEX OF THE
RIGHT ANGLE
INSIDE
NO SIGNIFICANCE
GIVEN
EQUIDISTANT TO THE
SIDES OF THE
TRIANGLE.
(The point is the center of
the inscribed circle.)
-BALANCING POINT
OF TRIANGLE
Significance of POC
-DIVIDES EACH
MEDIAN SO ONE
PIECE IS HALF THE
LENGTH OF THE
OTHER PIECE.
(2/3 and 1/3 of median)
EQUIDISTANT TO THE
VERTICES OF THE
TRIANGLE.
(The point is the center of
the circumscribed circle.)