Given: 22 3: 1 and 2 form a inear pair Prove: 1 and 23 are supplementary Statements Reosons 1.2 3 1. 2. m22 m3 2. 3. Z1 and 22 form a linear pair 4. 21 and 2 are supplementary 3. 4. 5. ml + m22 180 5. 6. mz1 +m23 180° 6. 7.21 and 23 are supplementary 7.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Postulates:
Properties of Congruence:
Angle Addifion Postulate
Refleive Property
Symmetric Property
Transifive Property
Theorems:
Vertical Angles Theorem
Complement Theorem
Linear Pair (Supplement) Theorem
Congruent Complements Theorem
Congruent Supplements Theorem
Definitions:
Definition of Congruence
Definition of a Right Angle
Definition of Complementary Angles
Definition of Supplementary Angles
Definition of an Angle Bisector
Definition of Perpendicular
S GUIDE
ANGLE PROOFS GUIDE
ocomplete proots 1-6.
nfor each prool.
Directions: Use the reasons below to complete proofs 1-6.
Cross them off as you use them for each proof.
ear Poir (Supplement)
• Linear Por (Supplement)
Theorem
• Definition of a Right Angle
• Definition of
Complementary Angles
. Given
Transitive Property
• Angle Addition Postulate
screm
• Substitution
Given
Dstitution
wen
Anition of Supplementary
oles
nition of Congruence
trillion of Supplementary
gles
wen
• Definition of Suppiementary
Angles
Defniton of Congruence
• Definition of Supplementary
Angles
• Given
drilion of Angie Bisector
won
wen
nsitive Property
dnition of Angle Boector
Given
• Congruent Complements
Theorem
. Complement Theorem
• Given
• Definition of Complementary
Angles
Definition of Angle Bsector
• Given
• Given
• Transitive Property
• Definition of Angle Bisector
linition of Congruence
ansitive Property
btraction Properny
wfinition of Complementary
ges
afeiton of Congruence
bstuton
alinition of Complementary
ngles
• Angle Addition Postulate
. Given
. Substitution
Delinifion of Congruence
Angle Addition Postulate
• harsitive Property
Defrition of Congruence
• Definition of Congruence
• Transitive Property
• Subtraction Property
• Defnition of Complementary
Angles
• Definition of Congruence
• Substitution
• Definition of Complementary
Angles
• Given
• Vertical Angles Theorem
• Given
Ven
articol Angles Theorem
ven
ANGs
Transcribed Image Text:Postulates: Properties of Congruence: Angle Addifion Postulate Refleive Property Symmetric Property Transifive Property Theorems: Vertical Angles Theorem Complement Theorem Linear Pair (Supplement) Theorem Congruent Complements Theorem Congruent Supplements Theorem Definitions: Definition of Congruence Definition of a Right Angle Definition of Complementary Angles Definition of Supplementary Angles Definition of an Angle Bisector Definition of Perpendicular S GUIDE ANGLE PROOFS GUIDE ocomplete proots 1-6. nfor each prool. Directions: Use the reasons below to complete proofs 1-6. Cross them off as you use them for each proof. ear Poir (Supplement) • Linear Por (Supplement) Theorem • Definition of a Right Angle • Definition of Complementary Angles . Given Transitive Property • Angle Addition Postulate screm • Substitution Given Dstitution wen Anition of Supplementary oles nition of Congruence trillion of Supplementary gles wen • Definition of Suppiementary Angles Defniton of Congruence • Definition of Supplementary Angles • Given drilion of Angie Bisector won wen nsitive Property dnition of Angle Boector Given • Congruent Complements Theorem . Complement Theorem • Given • Definition of Complementary Angles Definition of Angle Bsector • Given • Given • Transitive Property • Definition of Angle Bisector linition of Congruence ansitive Property btraction Properny wfinition of Complementary ges afeiton of Congruence bstuton alinition of Complementary ngles • Angle Addition Postulate . Given . Substitution Delinifion of Congruence Angle Addition Postulate • harsitive Property Defrition of Congruence • Definition of Congruence • Transitive Property • Subtraction Property • Defnition of Complementary Angles • Definition of Congruence • Substitution • Definition of Complementary Angles • Given • Vertical Angles Theorem • Given Ven articol Angles Theorem ven ANGs
Given: 22 3: 21 and 22 form a linear par
Prove: 1 and 23 are supplementary
Statements
Reosons
1. 223
1.
2. m22= m23
2.
3. Z1 and 22 form a linear pair
4. Z1 and 2 are supplementary
3.
4.
5. m21 + m2 180
5.
6. m2l + m23 180
6.
7. 21 and 23 are supplementary
7.
Transcribed Image Text:Given: 22 3: 21 and 22 form a linear par Prove: 1 and 23 are supplementary Statements Reosons 1. 223 1. 2. m22= m23 2. 3. Z1 and 22 form a linear pair 4. Z1 and 2 are supplementary 3. 4. 5. m21 + m2 180 5. 6. m2l + m23 180 6. 7. 21 and 23 are supplementary 7.
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