www.iTutoring.com -­‐ NOTES The Orthocenter and Centroid of a Triangle Name _________________________________ Date ___________________ Period _______ When three or more lines intersect at one point, the lines
are said to be concurrent.
m
n
P
l
Orthocenter of a Triangle
The point of concurrency of the altitudes of a triangle.
Y
C
X
A
P
B
Z
Orthocenter of a Triangle
The point of concurrency of the altitudes of a triangle.
P
Y
Y
P
Y
X
X
Z
Orthocenter is inside
of ∆XYZ
Z
P
Orthocenter is on ∆XYZ
vertex X (the right angle)
X
Z
Orthocenter is outside
of ∆XYZ
Centroid of a Triangle
The point of concurrency of the medians of a triangle.
Y
C
P
A
X
B
Z
© iTutoring.com
The Orthocenter and Centroid of a Triangle Pg. 2 Centroid Theorem
The distance from the vertex to the centroid is two-thirds to the distance
from the vertex to the midpoint of the opposite side.
Y
C
A
P
X
B
Point P is the centroid of ∆XYZ
Z
Orthocenter of a Triangle
Centroid of a Triangle
The point of concurrency of the
altitudes of a triangle.
Y
The point of concurrency of the
medians of a triangle.
Y
P
X
P
Z
X
Z
© iTutoring.com
The Orthocenter and Centroid of a Triangle Pg. 3