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

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!)

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

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

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

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

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

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

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.

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”