Transcript Slide 1

Triangles
are cool!
What is a perpendicular bisector in a triangle?
goes through the midpoint and is perpendicular to the side
What do you call the
intersection of the
perpendicular bisectors?
midpoints
circumcenter
What do you call
the intersection of the
medians in a triangle?
centroid
What is a median in a triangle?
connects a vertex to the midpoint of the opposite side
Are the circumcenter and centroid the same point?
An altitude in a triangle goes through a vertex and
is perpendicular to the opposite side.
ALTITUDE
vertex
perpendicular
The intersection of the three altitudes in a triangle is
called the orthocenter.
That’s a fun word!
Where is the orthocenter in a triangle located?
C
Classify this triangle
by angles.
The altitudes go
through a vertex and
are perpendicular to
a side.
Where is the
orthocenter?
A
B
What about this triangle?
C
Classify this triangle
by angles.
The altitudes go
through a vertex and
are perpendicular to
a side.
Where is the
orthocenter?
A
B
And how about this one?
Notice that two of the
sides had to be
extended so that an
altitude could be drawn.
A
C
Classify this triangle
by angles.
The altitudes go
through a vertex and
are perpendicular to
a side.
Where is the
orthocenter?
B
Where is the orthocenter of an acute triangle located?
Inside the triangle
Where is the orthocenter of an obtuse triangle located?
Outside the triangle
Where is the orthocenter of a right triangle located?
On the right angle vertex
White Note Card:
altitude / orthocenter
An altitude in a triangle goes through a vertex and is
perpendicular to the opposite side.
The intersection of the three altitudes of the sides of a
triangle 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
A special segment is drawn in each triangle. Identify each
special segment.
What is XW?
X
Z
W
Y
MD is an altitude in ΔLMN. Find the value for each variable.
M
Find the value for a, c, n, and x.
LN = 4x - 1
a
c
x+1
(n² - n)°
x
L
D
x+5
N
Make a Venn diagram to compare perpendicular bisectors, medians,
and altitudes.
 bisectors
and Medians
only
Medians
True of medians only
Perpendicular
bisectors
True of  bisectors
only
True for all
three
Medians and
Altitudes only
Altitudes and
 bisectors only
True of altitudes only
Altitudes
Circumcenters,
centroids,
orthocenters some of the coolest
words I’ve ever said!