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