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Warm Up1.Give the restrictions on the third side
of the triangle if the first two sides are 18 and 30.
2. Find x and y for both figures.
55° 70°x
y
100°2x + 10
4y
80
1
CAAG Unit 7B
UNIT QUESTION: What are the properties and characteristics of polygons?Standard: MM1G1.e.
Today’s Question:What is the centroid of a triangle, and what is special about it?Standard: MM1G.3.e.
2
Special Special Segments in Segments in
TrianglesTriangles3
Median
MedianMedian
4
Altitude
AltitudeAltitude
5
Tell whether each red segment is an altitude of the triangle.The altitude is the “true height” of
the triangle.
6
Perpendicular Bisector
Perpendicular Perpendicular BisectorBisector
7
Tell whether each red segment is an perpendicular bisector of the triangle.
8
Angle Bisector
Angle BisectorAngle Bisector
9
Drill & Drill & PracticePractice
Indicate which special triangle segment the red line is based on the picture and markings
10
11
12
13
14
15
20 20
16
start at a vertex and bisect the opposite
side.
Median
17
The intersection of the medians is called the CENTROID.
How many medians does a triangle have?
18
Theorem 5.8
The length of the segment from the vertex to the
centroid is twice the length of the segment from the centroid to the midpoint.
19
A BF
X
E
C
D
20
A BF
X
E
C
D
21
In ABC, AN, BP, and CM are medians.
A
B
M
P E
C
NIf EM = 3, find EC.EC = 2(3)
Ex: 1
EC = 6
22
In ABC, AN, BP, and CM are medians.
A
B
M
P E
C
N
If EN = 12, find AN.AE = 2(12)=24
Ex: 2
AN = 36
AN = AE + ENAN = 24 + 12
23
Altitude
24
The intersection of the altitudes is called the ORTHOCENTER.
How many altitudes does a triangle have?
25
26
The intersection of the perpendicular bisectors is called the CIRCUMCENTER.
How many perpendicular
bisectors does a triangle have?
27
What is special about the
CIRCUMCENTER?
Equidistant to the vertices of the triangle.
28
Example 1:Point G is the circumcenter of the triangle. Find GB.
B
A
C
G
ED
F
2
5
7
7
29
Angle Bisector
30
The intersection of the angle bisectors is called the INCENTER.
How many angle bisectors does a triangle have?
31
What is special about the INCENTER?
Equidistant to sides of the triangle
32
Example 1:
Point N is the incenter of the triangle. Find the length of segment ON.
18
30 18
33
Memorize these!Memorize these!
MCAOABI
PBCC
Medians/Centroid
Altitudes/Orthocenter
Angle Bisectors/Incenter
Perpendicular Bisectors/Circumcenter
34
Will this work?Will this work?
MCAOABI
PBCC
My Cat
Ate Our
Apples But I
Prefer Blue Cheese Crumbles
35
Come up with your own!
36