Key Points of Concurrency in Triangles
Notes
points of concurrency
These are the facts you must memorize about the points of concurrency!
In
– located inside of an
acute
triangle
On
– located at the vertex of the right angle on a
right
triangle
Out
– located outside of an
obtuse
triangle
The INCENTER is always located inside the triangle!
•
The center of the circle is the point of concurrency of the
bisector of all three interior angles.
•
The perpendicular distance from the incenter to each
side of the triangle serves as a radius of the circle.
•
All radii in a circle are congruent.
•
Therefore the incenter is equidistant from all three sides
of the triangle.
INCENTER FACTS:
ALL IN
In
– located inside of an
acute
triangle
In
– located inside of a
right
triangle
In
– located inside of an
obtuse
triangle
CENTROID FACTS:
•
The centroid is the
point of concurrency
of the three
medians in a triangle.
•
It is the center of mass (center of gravity) and
therefore is
always located within the triangle
.
•
The
centroid
divides each median into a piece one-
third (centroid to side) the length of the median and
two-thirds (centroid to vertex) the length
.
In
– located inside of an
acute
triangle
On
– located on (at the midpoint of) the hypotenuse of a
right
triangle
Out
– located outside of an
obtuse
triangle
C
i
r
c
u
m
c
e
n
t
e
r
•
The
point of concurrency
of the three
perpendicular bisectors of a triangle is the
circumcenter
.
•
It is the center of the circle
circumscribed
about
the triangle, making the circumcenter
equidistant
from the three
vertices
of the triangle
.
•
The circumcenter is not always within the triangle
.
Understand the essential facts about points of concurrency within triangles. Learn about the Incenter located inside the triangle, the Centroid as the center of mass, and the Circumcenter as the point of concurrency of perpendicular bisectors. Memorize the characteristics and significance of these important points within geometric shapes.
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Presentation Transcript
Notes points of concurrency These are the facts you must memorize about the points of concurrency!
In located inside of an acute triangle On located at the vertex of the right angle on a right triangle Out located outside of an obtuse triangle
INCENTER FACTS: The center of the circle is the point of concurrency of the bisector of all three interior angles. The perpendicular distance from the incenter to each side of the triangle serves as a radius of the circle. All radii in a circle are congruent. Therefore the incenter is equidistant from all three sides of the triangle.
ALL IN In located inside of an acute triangle In located inside of a right triangle In located inside of an obtuse triangle
CENTROID FACTS: The centroid is the point of concurrency of the three medians in a triangle. It is the center of mass (center of gravity) and therefore is always located within the triangle. The centroid divides each median into a piece one- third (centroid to side) the length of the median and two-thirds (centroid to vertex) the length.
In located inside of an acute triangle On located on (at the midpoint of) the hypotenuse of a right triangle Out located outside of an obtuse triangle
Circumcenter Circumcenter The point of concurrency of the three perpendicular bisectors of a triangle is the circumcenter. It is the center of the circle circumscribed about the triangle, making the circumcenter equidistant from the three vertices of the triangle. The circumcenter is not always within the triangle.
