segments and angles 2.2 angle bisectors. activity on a sheet of paper, draw a segment and label it...
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Segments and Angles
2.2 Angle Bisectors
Activity
On a sheet of paper, draw a segment and label it segment AB.
Draw another segment starting at B and ending at C (to make an angle).
Fold the paper so that segment AB is on top of segment BC.
Use a protractor to measure all the angles involved. What do you notice?
Vocabulary
Angle Bisector – a segment, ray, line, or plane that intersects an angle into two congruent angles.
Bisect – a verb meaning to divide in half (two congruent pieces)
ABCbisectsBDA
B
C
D
Example 1
Ray BD bisects angle ABC.
Find
110ABCmDBCmandABDm
A D
B C
55
55
DBCm
ABDm
Example 2
Ray HK bisects angle GHJ.Find KHJmandGHKm
J
K
H G
J
K
H G
52
26GHKm 45KHJm
Example 3
MP bisects LMN and 46LMPm
Find PMNm LMNmand
L P
M N
4646
92
46PMNm 92LMNm
Is angle LMN acute, right, obtuse, or straight? Obtuse
Example 4
QS bisects PQR
Find SQPm PQRmand
R
S
Q
P29
Is angle PQR acute, right, obtuse, or straight?
R
S
Q
P
45
PS
Q R
60
Example 4
QS bisects PQR
Find SQPm PQRmand
R
S
Q
P29 29
58
Is angle PQR acute, right, obtuse, or straight?
AcuteR
S
Q
P
45
45
90
Right
PS
Q R
60
60
120
Obtuse
Example: Several Angles
In the kite, DAB is bisected byAC and BCD is bisected by CA
Find DABm and BCDm
A
B
D
C27
45
Example: Several Angles
In the kite, DAB is bisected byAC and BCD is bisected by CA
Find DABm and BCDm
A
B
D
C4545
2727
DABm )45(2 90BCDm )27(2 54
Let’s Try This As a Class
Page 63
Numbers 7 and 8 at the top of the page.
Assignment A
Pages 64 – 65
14 – 23
Example: Bisectors and Algebra
A D
B C
BD bisects ABCFind the value of x.
)16( x85
8516 x846 x
6
84x
14x
Example: Bisectors and Algebra
BD bisects ABCFind the value of x.
A
D
B C
)38( x
)9( x
xx 938 x3
Example: Bisectors and Algebra
BD bisects ABCFind the value of x.
A
D
BC
)12(x55
5512x43x
Assignment B
Pages 65 – 66
24 – 30, 32
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