Geometry
Chapter 5 Lesson 4
Use Medians and Altitudes
Learning Target
• We will use medians and altitudes of triangles.
Medians and Altitudes
• Median: A segment that goes from each point
(vertex) of the triangle to the midpoint of the
opposite side.
• Every triangle has three medians.
• Centroid: The point of concurrency of the
medians of a triangle. ( where all three
medians meet)
Medians and Altitudes (cont’d)
• Centroid Theorem: The centroid of a triangle is two
thirds of the distance from each vertex to the
midpoint of the opposite side.
• If M is the centroid of ∆ABC, AM = 2/3 AE, BM = 2/3 BC, and
B
FM = 2/3 FD
D
E
M
A
centroid
C
F
B
D
E
M
A
C
F
Using Centroid Theorem
• For extra help on this topic:
• Look at example 1 on page 319
• Look at example 2 on page 320
Lets try:
• Guided practice #1-3 on page 320 in the
middle of the page.
Medians and Altitudes (cont’d)
• Altitude: A segment joining the vertex of a
triangle to the line containing the opposite
side at 90°.
• Every triangle has three altitudes.
– Draw pictures
Theorem 5.9
• Just something to know: You do not have to
draw or write this:
– Concurrency of Altitudes of a triangle: The lines
containing the altitudes are concurrent ( meet at a
point)
• Orthocenter: The point of concurrency of the
altitudes of a triangle.
• Acute triangle the orthocenter is on inside of a
triangle.
• Right triangle the orthocenter is on the
triangle.
• Obtuse the orthocenter is on outside of
triangle.
Medians and Altitudes (cont’d)
• Find x and m 2 if MS is an altitude of ∆MNQ,
m  1 = 3x + 11 and m 2 = 7x + 9.
Q
M
R
2 1
S
3x +11 + 7x + 9 = 90
10x + 20 = 90
10x = 70
x=7
m 2 = 58°
N
Together let’s try:
• Page 322-323 # 3,5,7,9,13,15,17,21,25,35
Class work:: Assignment #3
to be finished at home if you do not complete it here!!
• Page 322-323 # 4, 6, 8, 10, 14, 16, 18, 19, 20,
24, 26, 27, 33, 34
• Page 325 46-55