Download Altitudes, Medians, Bisectors of Triangles

5.2
As we’re going
through these slides,
look for times when
we can write
equations:
_______= _______
Introduction to Special
Segments in Triangles
&
_______ = 90
Altitudes, Medians,
& Bisectors of Triangles
Perpendicular Bisector of A
triangle:
►Bisects
the side of the triangle &
►Makes a right angle.
►May or may not begin at a vertex
_______= _______
(segments)
&
_______ = 90
(angle)
Angle Bisector of A triangle:
►Bisects
the angle it’s drawn from.
►Always from the vertex to the side
opposite.
_______= _______
(angles)
m1 = m2
1
2
Altitude of A triangle:
height of a triangle.
► Always forms a right angle with the side
► The
it intersects
starts at a vertex and intersects
_______ = 90
the opposite side.
(angle)
► May be inside, outside or on the triangle.
► Always
Median of A triangle:
►Always
from the vertex to the
midpoint of the opposite side.
►
Bisects the side opposite the vertex.
_______= _______
(sides)
You Try!
► Identify
the following special segments in
A
the triangles.




Median ____
Perpendicular Bisector ____
Altitude ____
Angle Bisector ____
X
B
C
W
E
Y
V
D
Z
F
Example:
►
Find the value of the variable.
 1) Given: 𝐶𝑋 is an altitude of ABC.
A
 2) Given: 𝐵𝑉 is a median
of ABC.
2x - 4
V
X
(5x)
8y
C
B
Think About It…
► In
the picture 𝐴𝑊 is a perpendicular
bisector of the base.
 Can you prove the two triangles are congruent?
A
Explain which postulate you used.
 If mC = 65 and CB=23.
Find the following:
 mWAB = ____
 CW = _____
25
C
65
65
W
11.5
|----------------------------------|
23
B
Summing up
Cuts into 2
congruent parts
Forms right
angles
Perpendicular
bisector
Congruent segments
Yes
Median
Congruent segments
No
Altitude
None
Yes
Angle bisector
Congruent angles
No