Identify altitudes and medians of triangles Identify the orthocenter and centroid of a triangle Use triangle segments to solve problems Identify a midsegment of a triangle and use it to solve problems.

1. Obj. 21 Medians, Altitudes, Midsegments
The student is able to (I can):
• Identify altitudes and medians of triangles
• Identify the orthocenter and centroid of a triangle
• Use triangle segments to solve problems
• Identify a midsegment of a triangle and use it to solve
problems.

2. median
altitude
A segment whose endpoints are a vertex of
the triangle and the midpoint of the
opposite side.
A perpendicular segment from a vertex to
the line containing the opposite side.

3. centroid The intersection of the medians of a
triangle. It is also the cccceeeennnntttteeeerrrr ooooffff mmmmaaaassssssss for
the triangle.

4. Centroid Theorem
The centroid of a triangle is located
of the distance from each vertex to
the midpoint of the opposite side.
G
H
J
X Y
R
Z
= 2
2
GR GY
3
= 2
HR HZ
3
JR JX
3
=
2
3

5. orthocenter The intersection of the altitudes of a
triangle.

6. midsegment A segment that joins the midpoints of two
sides of a triangle.
H
O
T
I C
E
Points I, C, and E are
midpoints of DHOT.
IC, CE, and EI
are midsegments.

7. Triangle Midsegment Theorem
A midsegment of a triangle is parallel to
a side of the triangle, and its length is
half the length of that side.
H
O
T
I C
E
1
IC HT, IC HT
2
=

8. Examples Find each measure.
1. FE
FE = 2(LT) = 2(14)
= 28
2. mÐUFE
F
mÐUFE = mÐTSE
= 62º
3. UE
UE = 2(9) = 18
L
U
T
E
S
14444
66662222º
9
LT and TS
are midsegments.