Complete the proof that ATUW ARXV. W R Statement Reason WX UV Given 2. RX TU Given ST RS Given 4 SW = SV Given 5. RV = RS + SV TW = ST + SW 7. RV = ST + SW Substitution 8. RV = TW Transitive Property of Equality 9. VX = WX + VW Additive Property of Length 10 UW = UV + VW Additive Property of Length 11 VX = UV + VW Substitution 12 UW = VX 13 ATUW ARXV SSS

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.3: The Field Of Quotients Of An Integral Domain
Problem 6E
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Reflexive property of congruence, reflexive property of equality, substitution, transitive property of congruence, transitive property of equality, vertical angle theorem
Complete the proof that ATUW ARXV.
W
R
U
Statement
Reason
WX UV
Given
2.
RX TU
Given
ST RS
Given
4
SW SV
Given
5.
RV = RS + SV
TW = ST + SW
7.
RV = ST + SW
Substitution
8.
RV = TW
Transitive Property of Equality
VX = WX + VW
Additive Property of Length
10
UW = UV + VW
Additive Property of Length
11
VX = UV + VW
Substitution
12
UW = VX
13
ATUW ARXV
SSS
Transcribed Image Text:Complete the proof that ATUW ARXV. W R U Statement Reason WX UV Given 2. RX TU Given ST RS Given 4 SW SV Given 5. RV = RS + SV TW = ST + SW 7. RV = ST + SW Substitution 8. RV = TW Transitive Property of Equality VX = WX + VW Additive Property of Length 10 UW = UV + VW Additive Property of Length 11 VX = UV + VW Substitution 12 UW = VX 13 ATUW ARXV SSS
Complete the proof that ATUW ARXV.
R
Statement
Reason
1.
WX UV
Given
2.
RX TU
Given
3
ST RS
Given
4.
SW SV
Given
RV = RS + SV
Additive Property of Length
All right angles are congruent
Definition of angle bisector
Definition of equilateral triangle
Definition of midpoint
TW = ST +E SW
RV = ST + SW
RV = TW
Additive Property of Length
MA + XM = XA
10
UW = UV + VW
Additive Property of Length
11
VX = UV + VW
Substitution
12
UW = VX
13
ATUW E ARXV
SSS
6.
Transcribed Image Text:Complete the proof that ATUW ARXV. R Statement Reason 1. WX UV Given 2. RX TU Given 3 ST RS Given 4. SW SV Given RV = RS + SV Additive Property of Length All right angles are congruent Definition of angle bisector Definition of equilateral triangle Definition of midpoint TW = ST +E SW RV = ST + SW RV = TW Additive Property of Length MA + XM = XA 10 UW = UV + VW Additive Property of Length 11 VX = UV + VW Substitution 12 UW = VX 13 ATUW E ARXV SSS 6.
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