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

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Presentation transcript:

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

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? P M O J K 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 GD E F Conclusions: DE = EF = FG 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 D B If <ABC = <CBD, then BC is the bisector of <ABD

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

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

E A B C D If B & C trisect AD, do EB &EC trisect <AED? 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 StatementReason 1.DH = HF1. Given 2.H is midpoint 2. Def: if a point divides a segment into 2 = segments, it is the midpoint. G H F D E

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