brain strain find the value of x. x x x xx special segments in triangles
TRANSCRIPT
Brain Brain StrainStrain
Find the value of x.
x x x
xx
Special Special Segments in Segments in
TrianglesTriangles
Median
MedianMedian
Altitude
AltitudeAltitude
Tell whether each red segment is an altitude of the triangle.The altitude is the “true height” of
the triangle.
Perpendicular Bisector
Perpendicular Perpendicular BisectorBisector
Tell whether each red segment is an perpendicular bisector of the triangle.
Angle Bisector
Angle BisectorAngle Bisector
Drill & Drill & PracticePractice
Indicate which special triangle segment the red line is based on the picture and markings
20 20
Points of Points of ConcurrencyConcurrency
The intersection of the angle bisectors is called the INCENTER.
Equidistant to the sides
The intersection
of the altitudes is called the
ORTHOCENTER.
The intersection
of the medians is called the CENTROID.
Vertex to Centroid is Twice as Long as Centroid to Midpoint
The intersection
of the perpendicular
bisector is called the
CIRCUMCENTER.
Equidistant to the vertices
Memorize these!Memorize these!
MCAOABI
PBCC
Medians/Centroid
Altitudes/Orthocenter
Angle Bisectors/Incenter
Perpendicular Bisectors/Circumcenter
Will this work?Will this work?
MCAOABI
PBCC
My Cat
Ate Our
Apples But I
Prefer Blue Cheese Crumbles
Special Property Special Property of Mediansof Medians
Theorem
Vertex to CENTROID is
TWICE as long as CENTROID to
MIDPOINT
vertex
centroid
midpoint
A BF
X
E
C
D
A BF
X
E
C
D
In ABC, AN, BP, and CM are medians.
A
BM
P E
C
N
If EM = 3, find EC.
Ex: 1
In ABC, AN, BP, and CM are medians.
A
BM
P E
C
N
If EN = 12, find AN.
Ex: 2
In ABC, AN, BP, and CM are medians.
A
B
M
P E
C
N
If CM = 3x + 6, and CE = x + 12, what is x?
CM = CE + EM
Ex: 3