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8. Given:

8. Given:

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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8. Given: <HKJ is a straight angle Steps Reasons KI bisects «HKJ 1. «HKJ is a straight angle Given 2. Definition straight angle Given 3. KÍ bisects «HKJ 4. «IKJ = «IKH 5. mxIKJ = m<IKH Defintion of congruent Prove: <IKJ is a right angle 6. Angle Addition Postulate 7. m<IKJ +m<IKJ =180° Substitution 8. 2(m<IKJ)=180° Simplify 9. Division Prop 10. KIKJ is a right angle 9. Given: FD bisects EFC Steps 1. FD bisects <«EFC; FC Reasons FC bisects <DFB Given bisects «DFB 2. «EFD = <DFC , XDFC = «CFB Definition of Congruent Transitive Prop F 3. 4. m<EFD ==m<CFB 5. «EFD=<CFB B Prove: «EFD =«CFB 10. Given: <VWXY is a right angle Reasons Steps <WXY is a right angle Given Y 2. m<WXY =90° 3. mx2+m<3= m<WXY 4. m<2+m3=90° 5. <1=<3 m<1 = m<3 7. mx2+m<l=90° 3. Substitution w Given Prove: mx2+ mx1=90° Substitution
Transcribed Image Text:8. Given: <HKJ is a straight angle Steps Reasons KI bisects «HKJ 1. «HKJ is a straight angle Given 2. Definition straight angle Given 3. KÍ bisects «HKJ 4. «IKJ = «IKH 5. mxIKJ = m<IKH Defintion of congruent Prove: <IKJ is a right angle 6. Angle Addition Postulate 7. m<IKJ +m<IKJ =180° Substitution 8. 2(m<IKJ)=180° Simplify 9. Division Prop 10. KIKJ is a right angle 9. Given: FD bisects EFC Steps 1. FD bisects <«EFC; FC Reasons FC bisects <DFB Given bisects «DFB 2. «EFD = <DFC , XDFC = «CFB Definition of Congruent Transitive Prop F 3. 4. m<EFD ==m<CFB 5. «EFD=<CFB B Prove: «EFD =«CFB 10. Given: <VWXY is a right angle Reasons Steps <WXY is a right angle Given Y 2. m<WXY =90° 3. mx2+m<3= m<WXY 4. m<2+m3=90° 5. <1=<3 m<1 = m<3 7. mx2+m<l=90° 3. Substitution w Given Prove: mx2+ mx1=90° Substitution
4. Given: m<A+m<B =90°; «A= «C Reasons Steps 1. mA+m<B =90° Given 2. XA = «C 3. m<A= m«C Given B 4. Substitution Prove: m<C+m<B=90° 5. Given: <1 and <2 form a straight angle Steps 1. <1 and <2 form a straight angle Given Reasons 2. 2. m<ABC =180° Definition of Straight 1 Angle Angle Addition Postulate A 3. 4. Substitution Prove: m<1+ mx2=180° 6. Given: m«EAC=90° Steps 1. M☆EAC =90° Reasons Given D 2. Angle Addition Postulate 3. Substitution
Transcribed Image Text:4. Given: m<A+m<B =90°; «A= «C Reasons Steps 1. mA+m<B =90° Given 2. XA = «C 3. m<A= m«C Given B 4. Substitution Prove: m<C+m<B=90° 5. Given: <1 and <2 form a straight angle Steps 1. <1 and <2 form a straight angle Given Reasons 2. 2. m<ABC =180° Definition of Straight 1 Angle Angle Addition Postulate A 3. 4. Substitution Prove: m<1+ mx2=180° 6. Given: m«EAC=90° Steps 1. M☆EAC =90° Reasons Given D 2. Angle Addition Postulate 3. Substitution
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