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White Note Card:
altitude / orthocenter
An altitude in a triangle goes through a vertex and is
perpendicular to the opposite side.
The intersection is the orthocenter of the triangle.
orthocenter
Location:
acute triangle: inside
obtuse triangle: outside
right triangle: on right angle vertex
AE is an altitude.
What is true about
the diagram?
A
AE  BC
Is E a midpoint?
 BEA and CEA are
both right angles.
Could E be a midpoint?
B
E
C
What is XW?
X
Z
W
Y
What is an angle bisector?
An angle bisector divides an angle into two congruent angles.
How many angles are there in a triangle?
So, how many angle bisectors are there in a triangle?
The intersections of the three angle bisectors in a triangle is
called the incenter.
Where is the incenter of a triangle located?
White Note Card:
Angle bisector / incenter
An angle bisector in a triangle divides an angle into two
congruent angles.
The intersection is the incenter of the triangle.
It is always inside the
triangle.
incenter
AC is an angle bisector. What is true about the diagram?
BAC   DAC
B
Is C a midpoint?
C
A
Is AC  BD?
D
Identify the special segment(s) in each triangle.
incenter
Classify each triangle described below by angles. If it is
not possible to classify the triangle from the information
given, then your answer should be “not enough information”.
The circumcenter is outside the triangle
The circumcenter is on the triangle
The incenter is inside the triangle
The orthocenter is outside of the triangle
The orthocenter is the same as a vertex
The centroid is inside the triangle.
Circumcenters,
centroids,
orthocenters,
incenters - this is
good stuff!