Download x – 1

10-3 Concurrent Lines
Thrm: Bisectors of the
angles of a triangle
intersect in a point that is
equidistant from the three
sides of a triangle.
Where multiple lines
meet is called the point
of concurrency. The
lines that go through
that point are called
concurrent lines.
The point of
concurrency of angle
bisectors is called an
INCENTER
Justification, points on angle
bisector are equidistant to the
sides, then transitive.
Thrm: Perpendicular
bisectors of the sides of a
triangle intersect in a point
that is equidistant to all the
vertices.
The point of
concurrency of
perpendicular
bisectors is called a
CIRCUMCENTER
Justification, points on
perpendicular bisector
are equidistant to the
endpoints, then transitive.
So to help keep track of things, it’s like the
go with the other, angle bisectors
equidistant to sides. Perpendicular
bisectors equidistant to vertices.
Median – A
line from the
midpoint to
the vertex
Where they all meet is the CENTROID
The distance from the Centroid to the
vertex is 2\3 the median.
The distance from the Centroid to the
midpoint is 1\3 the median.
Thrm: Altitudes all meet at
point.
Nothing special about it.
The point of
concurrency of
altitudes is called an
ORTHOCENTER
Think
2 ,1
3 3
D
M
U
G
C
DU = 5
CU = 5
DC = 10
SM = 12
DS = 24
DM = 12
K
KS =
CS =
CK =
CM =
GM =
CG =
9
18
9
18
6
12
S
UG =
GS =
US =
DK =
6
12
18
9
DG = 6
GK = 3
MA = -7x
MB = x2 – 8
-7x = x2 – 8
M
A
0 = x2 + 7x – 8
0 = (x + 8)(x – 1)
x = -8, x = 1
B
WHAT IS M?
A letter.
An
incenter!
• HW #19: Pg 388: CE 1-3, WE 1-5, 8-16
• There are number style problems that can
show up on a test.