1. WARM UP!
1. Without using a protractor, determine the angle formed by the hands of a clock at 11:24.
164
2. Given: <WTV = 80
<STW = 40
Prove: <STV is obtuse

2. 1.5 Division of Segments and Angles
Bisection: a point (segment, ray or line) that divides a SEGMENT into two congruent segments BISECTS the segment.
Midpoint: point where a line segment is bisected into 2 congruent parts.(line has to be collinear!)

3. If OK = KP what conclusions can you make?J
Conclusions:
K is the midpoint of OP
JM is a bisector of OP
Point K bisects OP

4. Trisected: Three congruent parts
Trisection points: the two points at which the segment is divided into three equal parts. H
Conclusions:
DE = EF = FG
HE and HF trisect DG E D F G

5. Angle Bisector:
A ray that divides an angle into two congruent angles is an angle bisector.
bi means two
If <ABC = <CBD, then BC is the bisector of <ABD A C D B

6. Draw AB and AC so that each bisect <DAE
Example 1: D A C B
Example 2: A D B E C

7. R T S
If RS = ST is S the midpoint?
NO! Not collinear!

8. If B & C trisect AD, do EB & EC trisect <AED?
Not necessarily! Only if ADE is isosceles.

9. Prove: H is midpoint of DF
Given: DH = HF
Prove: H is midpoint of DF G F H D E
Statement Reason
DH = HF 1. Given
H is midpoint
2. Def: if a point divides a segment into 2 = segments, it is the midpoint.

10. Given: KO bisects <JKM
Find m<OKM
Draw and label what you know! J O
m<OKM = ½ m<JKM K M
= ½ (41 37’)
= 20½  18½ ’
= 20 48’ 30”