2.5: Algebraic Proof
Definitions:
Proof - argument that uses logic, definitions, properties and previously proven statements to show that the conclusion is true
Properties of Equality:
Addition Property of Equality - if a=b then a+c=b+c
Subtraction Property of Equality - if a=b. then a-c=b-c
Multiplication Property of Equality - if a=b, then ac=bc
Division Property of Equality - if a=b. then a/c=b/c
Reflexive Property of Equality- a=a
Symmetric Property of Equality - if a=b, then b=a
Transitive Property of Equality - if a=b and b=c, then a=c
Substitution Property of Equality - if a=b, then b can be substituted for a in any expression
Properties of Congruence:
Reflexive Property of Congruence - figure A is congruent to figure A
Symmetric Property of Congruence - if figure A is congruent to figure B, then figure B
is congruent to figure A
Transitive Property of Congruence - if figure A is congruent to figure B and figure B is
congruent to figure C, then figure A is congruent to figure C
Examples:
Definitions:
Proof - argument that uses logic, definitions, properties and previously proven statements to show that the conclusion is true
Properties of Equality:
Addition Property of Equality - if a=b then a+c=b+c
Subtraction Property of Equality - if a=b. then a-c=b-c
Multiplication Property of Equality - if a=b, then ac=bc
Division Property of Equality - if a=b. then a/c=b/c
Reflexive Property of Equality- a=a
Symmetric Property of Equality - if a=b, then b=a
Transitive Property of Equality - if a=b and b=c, then a=c
Substitution Property of Equality - if a=b, then b can be substituted for a in any expression
Properties of Congruence:
Reflexive Property of Congruence - figure A is congruent to figure A
Symmetric Property of Congruence - if figure A is congruent to figure B, then figure B
is congruent to figure A
Transitive Property of Congruence - if figure A is congruent to figure B and figure B is
congruent to figure C, then figure A is congruent to figure C
Examples: