1. Division of Segments & Angles.
Geometry 1.5

2. Definition: SEGMENT BISECTOR
Is a point, segment, ray, or line that divides a segment into 2 segments.
a. If a segment (or line or ray) bisects a segment, then it forms 2 congruent segments.
b. If a segment (or line or ray) divides a segment into 2 congruent segments, then it bisects the segment.

3. Definition: SEGMENT TRISECTORS
Are 2 points, lines, segments, or rays that divide a segment into 3 segments.

4. Definition: MIDPOINT Is a point that divides a segment into 2
segments.

5. Definition: ANGLE BISECTOR: Is a ray that divides an angle into 2
angles.

6. Definition: ANGLE TRISECTORS
Are 2 rays that divide an angle into 3 angles.

7. Only segments have midpoints (not lines or rays)
CAUTION
Only segments have midpoints (not lines or rays)
Questions:
For a given segment, how many midpoints exist?
For a given segment how many bisectors exist?

8. EXAMPLES

9. 1.

10. Given: bisects <BAC. m<1 = 2x + 8 m<2 = x + 20
Find: a. m<1
b. m<BAC
2x + 8 = x x - 8 = -x – x = 12
2(12) + 8 = 32º= m<1
m<BAC = <1+< = = 64º

11. 3. Bisects <BAC = 20º20’ = 40º40’ = 49º40’ = 22º31’30”
a. If m<1 = 20º20’, what is m<2?
= 20º20’
b. If m<1 = 20º20’, what is m<BAC?
=20º20’ + 20º20’
= 40º40’
c. If m<1 = 24º50’, what is m<BAC?
=24º50’ + 24º50’
= 49º40’
d. If m<BAC = 45º3’, what is <1?
=45º3’÷2
= 22º31’30”

12. Prove: bisects <AOD
Given:
Prove: bisects <AOD
Statements
Reasons 1.
1. Given
2. If a ray divides an angle into two congruent angles, then it bisects the angle. 2.
bisects <AOD

13. 7. Given: is divided by points B,C such that AB:BC:CD=4:1:3
7. Given: is divided by points B,C such that AB:BC:CD=4:1:3. If AD=40, find the length of AC.
8. Given:
If the larger of the two numbered angles is 20 more than one half the smaller, is acute or obtuse?