Transcript ALTITUDES, MEDIANS AND BISECTORS PowerPoint

SECTION 5-1
spi.3.2.J
Jim Smith JCHS
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.
Start at a vertex and form a 90° angle
with the line containing the opposite side.
Orthocenter
The orthocenter can be located
in the triangle, on the triangle or
outside the triangle.
Obtuse
Right
Legs are altitudes
Angle bisectors start at a vertex
and bisect the angle.
Incenter
Any point on an angle bisector is
equidistance from the sides of the angle
This makes the Incenter an
equidistance from all 3 sides
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
Any point on the perpendicular bisector
of a segment is equidistance from the
endpoints of the segment.
A
C
AB is the perpendicular
bisector of CD
D
B
This makes the Circumcenter an
equidistance from the 3 vertices
The median starts at a vertex and ends
at the midpoint of the opposite side.
Centroid
The centroid is 2/3’s of the distance
from the vertex to the side.
10
2x 32
5x
16
X
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
Altitude ..
Vertex .. 90° .. Orthocenter
Angle Bisector..
Angle into 2 equal angles .. Incenter
Perpendicular Bisector…
90° .. bisects side .. Circumcenter
Median ..
Vertex .. Midpoint of side ..Centroid
Give the best name for AB
A
|
A
|
A
B
B
B
Median Altitude None
A
A
|
|
B
B
Angle
Perp
Bisector Bisector
Survival Training
You’re Stranded On A Triangular
Shaped Island. The Rescue Ship Can
Only Dock On One Side Of The Island
But You Don’t Know Which Side. At
Which Point Of Concurrency Would
You Set Up Camp So You Are An
Equal Distance From All 3 Sides?
INCENTER
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
Where would you place a fire hydrant to
make it equidistance to the houses and
equidistance to the streets?
POST
Angle bisector for the streets
Perpendicular bisector for houses
POST