altitudes

1
altitudes
bisectors
medians
SECTION 5-1 spi.3.2.J
Jim Smith JCHS
2
There are 3 of each of these special segments in
a triangle. The 3 segments are concurrent.
They intersect at the same point. This point is
called the point of concurrency. The points
have special names and special properties.
3
Altitudes
Start at a vertex and form a 90 angle with the
line containing the opposite side.
Orthocenter
4
The orthocenter can be located in the triangle,
on the triangle or outside the triangle.
Obtuse
Right
Legs are altitudes
5
Angle Bisectors
Angle bisectors start at a vertex and bisect the
angle.
Incenter
6
Any point on an angle bisector is equidistance
from the sides of the angle
7
This makes the Incenter an equidistance from all
3 sides
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Perpendicular Bisectors
A Perpendicular bisector of a side does not have
to start at a vertex. It will form a 90 angles
and bisect the side.
Circumcenter
9
Any point on the perpendicular bisector of a
segment is equidistance from the endpoints of the
segment.
AB is the perpendicular bisector of CD
A
C
D
B
10
This makes the Circumcenter an equidistance from
the 3 vertices
11
Median
The median starts at a vertex and ends at the
midpoint of the opposite side.
Centroid
12
The centroid is 2/3s of the distance from the
vertex to the side.
32
10
2x
5
x
X
16
13
The centroid is the center of balance for the
triangle. You can balance a triangle on the tip
of your pencil if you place the tip on the
centroid
14
Quick notes
Altitude .. Vertex .. 90 .. Orthocenter Angle
Bisector.. Angle into 2 equal angles ..
Incenter Perpendicular Bisector 90 .. bisects
side .. Circumcenter Median .. Vertex ..
Midpoint of side ..Centroid
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Median Altitude None Angle Perp
Bisector
Bisector
16
Survival Training
Youre Stranded On A Triangular Shaped Island.
The Rescue Ship Can Only Dock On One Side Of The
Island But You Dont Know Which Side. At Which
Point Of Concurrency Would You Set Up Camp So
You Are An Equal Distance From All 3 Sides?
INCENTER
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What If The Ship Could Only Dock At One Of The
Vertices? Would You Change The Location Of Your
Camp ? If So, Where?
YES
CIRCUMCENTER
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Where would you place a fire hydrant to make it
equidistance to the houses and equidistance to
the streets?
ELM
POST
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Angle bisector for the streets Perpendicular
bisector for houses
ELM
POST