Download 5.4 Triangle Medians and Altitudes Classwork A median of a triangle

5.4 Triangle Medians and Altitudes Classwork
A median of a triangle is a segment that connects a ___________________ of a triangle to the ____________________.
Their point of concurrency is called the ________________________.
1.
2.
3.
4.
5.
Find the midpoint of AB, BC, and AC. Label the midpoints as X, Y, and Z, respectively.
Draw the three medians of the triangle. Label the point of concurrency T.
Find the measure of XC. ___________ Find the measure of TX. _________________.
Find the measure of AY. ___________ Find the measure of TY. _________________.
Find the measure of ZB. ___________ Find the measure of TZ. _________________.
What is the relationship between the measures of the segments?
A
B
C
Theorem: The centroid divides the medians of a triangle such that


The centroid to the midpoint is one-third of the length of the entire length of the median.
The centroid to the vertex of the triangle is two-thirds the length of the entire length of the median.
An Altitude is a segment that is _________________________ from a vertex to its opposite side.
Draw the three altitudes of triangle ABC.
A
B
C
The point of concurrency of the altitudes of a triangle is called the _________________________________.
Directions: Use the diagram shown and the given information to match the type of special segment with the correct
A
segment.
BAE  EAC and BF  FC
1) median
A. AD
2) altitude
B. AE
3) perpendicular bisector
C. AF
4) angle bisector
D. GF
G
B
D
C
F
E
5) Use the diagram and given information to decide in each case if WY is either:
- a perpendicular bisector
- an altitude
- an angle bisector
- a median
a) YX  YZ
X
b) XWY  ZWY
Y
c) YX  YZ and WY  XZ
d) WY  XZ
6) R is the centroid of ∆STU and UV=11, RU=8, and SR=10.
VT = ________________
Z
W
T
VS = ________________
V
RW = _______________
UW = _______________
R
W
U
X
7) C is the centroid of ∆XYZ, YK=12, XC=10, YI= 9 and XK  YZ .
S
X
CK = ________________
XK= ________________
YC = _______________
I
J
C
KZ = _______________
JZ = _______________
Y
Z
K
B
4.
5.
80°
10
L
T
M
6.
9
A
60°
40°
8
14
6
C
S
K
R
Name the sides shortest
to longest.
Name the angles smallest
to largest.
______, ______, ______
______, ______, ______
7. Decide whether the given sides form a triangle: 4, 4, 8.
5
Name the angles smallest
to largest.
______, ______, ______