Complete the following proof to pro Given Prove Reflexive Property of Equality Vertical angles are congruent Given: /1 and 23 are vertical an Transitive Property of Equality Prove: Z1 23 Angles that form a linear pair are supplementary angles Statements Definition of congruent angles 1. Z1 and 23 are vertical angles. 2. Z1 and 2 are supplementary. Subtraction Property of Equality Definition of supplementary angles 22 and 23 are supplementary. 3. m/1+m/2 = 180 3. Definition of supplementary angles m/2+m/3 = 180 4. 4. Transitive property of Equality m/1+m/2 =m/2+m/3 5. Subtraction property of equality 6. Definition of congruent angles 5. m/1= m/3 6. Z1 23
Complete the following proof to pro Given Prove Reflexive Property of Equality Vertical angles are congruent Given: /1 and 23 are vertical an Transitive Property of Equality Prove: Z1 23 Angles that form a linear pair are supplementary angles Statements Definition of congruent angles 1. Z1 and 23 are vertical angles. 2. Z1 and 2 are supplementary. Subtraction Property of Equality Definition of supplementary angles 22 and 23 are supplementary. 3. m/1+m/2 = 180 3. Definition of supplementary angles m/2+m/3 = 180 4. 4. Transitive property of Equality m/1+m/2 =m/2+m/3 5. Subtraction property of equality 6. Definition of congruent angles 5. m/1= m/3 6. Z1 23
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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Transcribed Image Text:Complete the following proof to prove the Vertical Angles Theorem
Given: 21 and 23 are vertical angles.
Prove: /12 23
Statements
Reasons
1. Z1 and 23 are vertical
1. Given
angles.
2. Z1 and 22 are
supplementary.
2.
/2 and 23 are
supplementary.
3. m/1+m/2
180
3. Definition of supplementary angles
m/2+m/3
= 180
4.
4. Transitive property of Equality
m/1+m/2 = m/2+mZ3
5. m/1 = m/3
5. Subtraction property of equality
6. Definition of congruent angles
6. Z12 23
Transcribed Image Text:Complete the following proof to pro
Given
Prove
Reflexive Property of Equality
Vertical angles are congruent
Given: 21 and 23 are vertical an Transitive Property of Equality
Prove: Z12 23
Angles that form a linear pair are supplementary angles
Statements
Definition of congruent angles
1. Z1 and Z3 are vertical
angles.
Subtraction Property of Equality
2. Z1 and 2 are
Definition of supplementary angles
supplementary.
/2 and 23 are
supplementary.
3. m/1+m/2 = 180
3. Definition of supplementary angles
m/2+m/3 = 180
4. Transitive property of Equality
m/1+m/2 =m/2+mZ3
5. m/1 = m23
5. Subtraction property of equality
6. Z12 23
6. Definition of congruent angles
4.
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