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Geometry Concepts Illustrated with Clocks and Protractors

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Explore concepts like trisection, bisection, and angle bisectors in geometry using clock angles and protractors without direct measurements. Learn key geometric properties and relationships in a visual and practical way.

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Geometry Concepts Illustrated with Clocks and Protractors

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  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? M O K P 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 B C A E Example 2: B E D A 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? A E B C D Not necessarily! Only if ADE is isosceles.

  9. Given: DH = HF Prove: H is midpoint of DF G F H D E StatementReason 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 <JKM = 41 37’ 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”

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