Transcript Special Segments in Triangles

Special Segments in
Triangles
Section 5-1
Perpendicular Bisector a line or line segment that passes
through the midpoint of a side of
a triangle and is perpendicular to
that side of the triangle
XY is
of AB
X
A
Y
B
bisector
Theorem 5-1
• Any point on the
perpendicular bisector of
a segment is equidistant
from the endpoints of the
segment.
Theorem 5-2
• Any point equidistant
from the endpoints of a
segment lies on the
perpendicular bisector of
the segment.
CD is a perpendicular bisector
of AB.
C
X
A
AX = XB
B
D
Median a segment that connects a vertex
of a triangle to the midpoint of
the side opposite that vertex.
B
BZ is a median.
A
Z
C
Altitude a segment drawn from the vertex
of a triangle perpendicular to the
opposite side
B
A
X
BX is an altitude
C
Theorem 5-4
• Any point on the bisector
of an angle is equidistant
from the sides of the
angle.
Theorem 5-5
• Any point equidistant
from the sides of an angle
lies on the bisector of the
angle.
ZB is an angle bisector.
XM = MY
Z
A
C
X
Y
B
Joke Time
What tool do you use
in Algebra?
multi-pliers
There are 2 men on 2 different
trains on the opposite sides of a 10
mile railroad track. One train is
traveling 50 mph and the other train
is traveling 40 mph. Where will
they meet?
in the hospital