Download 5.3 Concurrent lines

5.3
Concurrent
Lines,
Medians, and
Altitudes
First things first
New words:
Concurrent means when three or more
lines intersect in one point.
Point of concurrency
Now, a theorem to go along with concurrent.
The perpendicular bisectors of the sides of a
triangle are concurrent at a point
equidistant from the vertices.
More new words
The point of concurrency of the
perpendicular bisectors of a
triangle is called the
circumcenter of the triangle
More new words
The circle is circumscribed
about the triangle.
Lets try one
Bisect theHow
sidesdo you find the
center for the circle
of the triangles
circumscribed about the
triangle.
(-.5,1)
Just another theorem
The bisectors of the angles of a triangle are
concurrent at a point equidistant from the
sides.
More new words
The point of concurrency of the
angle bisectors of a triangle is
called the incenter of the
triangle.
More new words
The circle is inscribed in the
triangle.
More new words
A median of a triangle is a
segment whose endpoints are a
vertex and the midpoint of the
opposite side.
Looks like another theorem
The medians of a
triangle are concurrent
at a point that is two
thirds the distance from
each vertex to the
midpoint of the opposite
side.
B
CG=2/3CD
2/ AE
AG=
3
E
centroid D
2/ BF
BG=
3
G
A
F
C
Lets try one
Find FB when BG=6
B
E
D
G
A
F
C
BG=2/3BF
6=2/3BF
3/ (6)= 3/ (2/ BF)
2
2
3
18/
2=BF
9=BF
An altitude of a
triangle is the
perpendicular segment
from a vertex to the
line containing the
opposite side.
We’re
Almost
done
One more theorem
The line that contain
the altitudes of a
triangle are
concurrent at the
ORTHOCENTER.
We’re
Almost
done
Here comes the
assignment
Assignment
Workbook
Page 343 all