Download Ch 5 Special Segments and Points of Concurrency in Triangles

Ch 5
Special Segments
and
Points of Concurrency
in
Triangles
Perpendicular Bisector: a segment that is a
part of the bisector of one of the sides
of a triangle.
T
[Look for 90o and midpoint (≅ segments)
All about altitudes
1
Point of concurrency: CIRCUMCENTER
Location:
Acute: inside
Right: on
Obtuse: outside
Vertex as endpoint: sometimes
Special Properties: the point of concurrency
is equidistant from the vertices.
Illustrations:
l
B
lll
l
D
lll
A
E
C
ll
ll
circumcenter
2
Angle Bisector: a segment that bisects 1 of
the angles of a triangle.
[Look for ≅ angles
All about altitudes
Point of concurrency: INCENTER
Location:
Acute: inside
Right: inside
Obtuse: inside
Vertex as endpoint: always
Special Properties: the point of concurrency
is equidistant from the 3 sides of the r.
3
Illustrations:
B
E
A
C
incenter
Median: a segment whose endpoints are a
vertex and the midpt of the opposite side.
[Look for vertex & midpoint (≅ segments)
All about altitudes
4
Point of concurrency: Centroid
Location:
Acute: inside
Right: inside
Obtuse: inside
Vertex as endpoint: always
Special Properties: the point of concurrency
is 2/3 of the distance from the vertex to
the midpoint of the opposite side.
Illustrations:
B
D
A
C
centroid
5
Altitude: a segment from the vertex that is
to the opposite side.
(also known as the height for the triangle)
T
[Look for vertex & right L (90o)
All about altitudes
Point of concurrency: orthocenter
Location:
Acute: inside
Right: on
Obtuse: outside
Vertex as endpoint: always
Special Properties: none
6
Illustrations:
orthocenter
If a segment is coming from the vertex angle
of an isosceles triangle and it is identified as
one of the "special" segments, then it is all 4
types.
vertex angle
perp bisector
angle bisector
median
altitude
base angles
7
If the triangle is equilateral, then all 3
segments from the vertex are all 4 special
segments.
Centroid:
C
B
A
K
F
D
E
CK
8
Identify all the special segments.
Given: G is the midpoint of AF
Altitude: _______
bisector: _____
T
L bisector: _____
Median: _______
C D
E
B
A
H G
F
HW pg 275 #14­17 pg 280 #1­6, 10­14
9
TOTD
C
B
A
10
CK
K
D
F
E
7
What is the difference between an
altitude and perpendicular bisector?
10