TW bisects ZUWY and ZX ZV. Complete the proof that ATWX ATWV. T. U W V Statement Reason TW bisects ZUWY Given 2 ZX E ZV Given ZXWY ZUWV Vertical Angle Theorem 4 ZTWY E ZTWU M2TWX = MZTWY + MZXWY Angles forming a linear pair sum to 180° Definition of angle bisector Definition of equilateral triangle Definition of midpoint Vertical Angle Theorenm 6 M2TWV = MZTWU + mZUWV M2TWX = M2TWU + mZUWV M2TWV = MZTWX 6. TW TW Reflexive Property of Congruence 10 ATWX ATWV AAS
TW bisects ZUWY and ZX ZV. Complete the proof that ATWX ATWV. T. U W V Statement Reason TW bisects ZUWY Given 2 ZX E ZV Given ZXWY ZUWV Vertical Angle Theorem 4 ZTWY E ZTWU M2TWX = MZTWY + MZXWY Angles forming a linear pair sum to 180° Definition of angle bisector Definition of equilateral triangle Definition of midpoint Vertical Angle Theorenm 6 M2TWV = MZTWU + mZUWV M2TWX = M2TWU + mZUWV M2TWV = MZTWX 6. TW TW Reflexive Property of Congruence 10 ATWX ATWV AAS
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter10: Analytic Geometry
Section10.CT: Test
Problem 21CT
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Question
Transcribed Image Text:TW bisects ZUWY and ZX ZV. Complete the proof that ATWX ATWV.
Y
U
W
V
Statement
Reason
1
TW bisects ZUWY
Given
2
ZX E ZV
Given
ZXWY ZUWV
Vertical Angle Theorem
4
ZTWY E ZTWU
M2TWX = MZTWY + MZXWY
Angles forming a linear pair sum to 180°
Definition of angle bisector
Definition of equilateral triangle
Definition of midpoint
Vertical Angle Theorenm
Reflexive Property of Congruence
6
M2TWV = MZTWU + mZUWV
M2TWX = M2TWU + mZUWV
M2TWV = M2TWX
6.
TW TW
10
ATWX ATWV
AAS
3.
Transcribed Image Text:TW bisects LUWY and ZX- ZV. Complete the proof that ATWX ATWV.
U
V
Statement
Reason
Given
TW bisects ZUWY
Given
2
ZX E ZV
Vertical Angle Theorem
ZXWY E ZUWV
4
ZTWY LTWU
Additive Property of Angle Measure
Additive Property of Length
All right angles are congruent
Angles forming a linear pair sum to 180°
Definition of angle bisector
Dofinition nf mouilata-al trinnala
Transitive Property of Equality
MZTWX = MZTWY + mZXWY
MZTWV = MLTWU + m2UWV
MZTWX = M2TWU + m2UWV
MZTWV = MZTWX
TW TW
Reflexive Property of Congruence
10
ATWX E ATWV
AAS
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