Reason FI bisects ZGIK Given FI bisects ZHFJ Given ZJIK E ZGIH Vertical Angle Theorem ZFIK E ZFIG Definition of angle bisector ZIFJ ZHFI Definition of angle bisector MLFIJ = MZFIK + mZJIK Additive Property of Angle Measure MLFIH = MZFIG + MZGIH Definition of angle bisector Definition of equilateral triangle Definition of midpoint Reflexive Property of Congruence Reflexive Property of Equality MLFIJ = mZFIG + MZGIH MLFIH = MZFIJ Fe可 AFHI = AFJI ASA

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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Question
Substitution, transitive property of equality, transitive property of congruence, vertical angle theorem.
FI bisects ZGIK and ZHFJ, Complete the proof that AFHI = AFJI.
Statement
Reason
FI bisects ZGIK
Given
FI bisects ZHEJ
Given
ZJIK E ZGIH
Vertical Angle Theorem
4
ZFIK ZFIG
Definition of angle bisector
ZIFJ E ZHFI
Definition of angle bisector
MLFIJ = mZFIK + MZJIK
Additive Property of Angle Measure
7
MZFIH = MZFIG + MZGIH
Definition of angle bisector
Definition of eguilateral triangle
Definition of midpoint
Reflexive Property of Congruence
Reflexive Property of Equality
MLFIJ = mZFIG + MZGIH
MLFIH = MZFIJ
10
Fe可
11
AFHI E AFJI
ASA
2.
Transcribed Image Text:FI bisects ZGIK and ZHFJ, Complete the proof that AFHI = AFJI. Statement Reason FI bisects ZGIK Given FI bisects ZHEJ Given ZJIK E ZGIH Vertical Angle Theorem 4 ZFIK ZFIG Definition of angle bisector ZIFJ E ZHFI Definition of angle bisector MLFIJ = mZFIK + MZJIK Additive Property of Angle Measure 7 MZFIH = MZFIG + MZGIH Definition of angle bisector Definition of eguilateral triangle Definition of midpoint Reflexive Property of Congruence Reflexive Property of Equality MLFIJ = mZFIG + MZGIH MLFIH = MZFIJ 10 Fe可 11 AFHI E AFJI ASA 2.
FI bisects ZGIK and ZHFJ. Complete the proof that AFHI - AFJI.
H.
Statement
Reason
1.
FI bisects ZGIK
Given
FI bisects ZHFJ
Given
ZJIK E LGIH
Vertical Angle Theorem
4
ZFIK E ZFIG
Definition of angle bisector
ZIF) E ZHFI
Definition of angle bisector
6
MZFIJ = MZFIK + M2JIK
Additive Property of Angle Measure
MZFIH = mZFIG + MZGIH
Additive Property of Angle Measure
Additive Property of Length
Algebra
All right angles are congruent
Angles forming a linear pair sum to 180°
Dafinitia nof asala hicacta
ASA
MZFIJ = MZFIG + M2GIH
MZFIH = MZFIJ
10
Fi Fi
11
AFHI E AFJI
Transcribed Image Text:FI bisects ZGIK and ZHFJ. Complete the proof that AFHI - AFJI. H. Statement Reason 1. FI bisects ZGIK Given FI bisects ZHFJ Given ZJIK E LGIH Vertical Angle Theorem 4 ZFIK E ZFIG Definition of angle bisector ZIF) E ZHFI Definition of angle bisector 6 MZFIJ = MZFIK + M2JIK Additive Property of Angle Measure MZFIH = mZFIG + MZGIH Additive Property of Angle Measure Additive Property of Length Algebra All right angles are congruent Angles forming a linear pair sum to 180° Dafinitia nof asala hicacta ASA MZFIJ = MZFIG + M2GIH MZFIH = MZFIJ 10 Fi Fi 11 AFHI E AFJI
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