WARM UP 1 Without using a protractor determine

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

1. 5 Division of Segments and Angles Definition: 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? O J M K P Conclusions: K is the midpoint of OP JM is a bisector of OP Point K bisects OP

Trisected: 3 congruent parts Trisection points: the 2 points at which the segment is divided into three equal parts. H Conclusions: DE = EF = FG D E F G HE and HF trisect DG

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

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

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

If B & C trisect AD, do EB &EC trisect <AED? A E B C D NO! Just because AD is trisected it doesn’t mean that the < is trisected! We can’t assume it!!! The triangle needs to be isosceles!

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

Given: KO bisects <JKM = 41 37’ Find m<OKM Draw and label what you know! m<OKM = m<JKM = = 20 O K (41 37’) 18 J ’ = 20 48’ 30” M