Special Segments in Triangles

1
Special Segments in Triangles

• Section 5-1

2
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 bisector of AB
X
A
B
Y
3
Theorem 5-1

• Any point on the perpendicular bisector of a
  segment is equidistant from the endpoints of the
  segment.

4
Theorem 5-2

• Any point equidistant from the endpoints of a
  segment lies on the perpendicular bisector of the
  segment.

5

• CD is a perpendicular bisector of AB.

C
AX XB
X
A
B
D
6
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
C
Z
7
Altitude -

• a segment drawn from the vertex of a triangle
  perpendicular to the opposite side

B
BX is an altitude
A
C
X
8
Theorem 5-4

• Any point on the bisector of an angle is
  equidistant from the sides of the angle.

9
Theorem 5-5

• Any point equidistant from the sides of an angle
  lies on the bisector of the angle.

10
ZB
is an angle bisector. XM MY
Z
A
C
X
Y
B
11
Joke Time

• What tool do you use in Algebra?
• multi-pliers

12

• 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