1.5 Segment &
Angle Bisectors
Geometry
Mrs. Blanco
Standard/Objective
Standard 3: Students will understand
geometric concepts and applications.
Objectives:
• Find the Midpoint of a segment.
• Bisect a segment.
• Bisect an angle.
Midpoint
• The point on a segment that divides the
segment into two congruent segments.
(bisects a segment)
 x1  x2 y1  y2 
,


2 
 2
Ex 1a: Find the midpoint of CD if
C(-12,-9) & D(2,10).
 12  2 9  10 
,


2
2 

 10 1 
, 

2
 2
1

 5, 
2

Ex 1b: You Try:
Find the Midpoint of CD
C(-1.5,4) & D(0.25,-1).
Ex 2a: The midpoint of BD is M(-1,1). One
endpoint is D(2,6).
Find the coordinates of B.
D
M
B(-4,-4)
Ex 2b: You Try:
Find the B if
M(0,3) & D(-8,-1)
Segment Bisector
• A segment, ray, line, or plane that
intersects a segment at its midpoint.
k
A
M
B
Angle Bisector
• A ray that divides an angle into two adjacent
angles that are congruent.
A
D
B
C
BD is an angle
bisector of  ABC.
Ex 3a: If QS bisects PQR &
mSQR=22o, what is mPQR
and mPQS ?
mPQS=22°
mPQR=44°
Ex 3b: If QS bisects PQR &
mPQR=124o, what is mPQS
and mSQR ?
mPQS=62°
mSQR=62°
Ex 4a: If RQ bisects PRS.
Solve for x
mÐPRQ = mÐQRS
x+40 = 3x-20
40 = 2x-20
60 = 2x
30 = x
Last Example:
Ex 4b: If BD bisects ABC.
Solve for x
1/2x+20 = 3x-85
20 = 2 ½ x-85
105 = 2 ½ x
42 = x
•Class practice—
•Pgs. 38-40
•#18, 22, 26, 28, 32,
38, 39, 40, 41, 44,
46, 48, 52, 54,