Obj. 7 Algebraic Proof proof – an argument which uses logic, definitions, properties, and previously proven statements algebraic proof – A proof which uses algebraic properties • When you write a proof, you must give a justification (reason) for each step to show that it is valid. For each justification, you can use a definition, postulate, property, or a piece of given information.
Obj. 7 Algebraic Proof
Jan 02, 2016
Obj. 7 Algebraic Proof. proof – an argument which uses logic, definitions, properties, and previously proven statements algebraic proof – A proof which uses algebraic properties - PowerPoint PPT Presentation
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Obj. 7 Algebraic Proof
proof – an argument which uses logic, definitions, properties, and previously proven statements
algebraic proof – A proof which uses algebraic properties
• When you write a proof, you must give a justification (reason) for each step to show that it is valid. For each justification, you can use a definition, postulate, property, or a piece of given information.
Algebraic Properties Foldable• Make a hotdog fold.• Make shutters.• Open up all the folds and make a hamburger
fold.• Make shutters.• Cut from the edge of the paper to the fold on
each side. This should give you eight sections.
Addition Property of
Equality
Subtraction Property of
Equality
Multiplication Property of
Equality
Division Property of
Equality
Reflexive Property of
Equality
Symmetric Property of
Equality
Transitive Property of
Equality
Substitution Property of
Equality
If a = b, thena + c = b + c(add. prop.
=)
Subtraction Property of
Equality
Multiplication Property of
Equality
Division Property of
Equality
Reflexive Property of
Equality
Symmetric Property of
Equality
Transitive Property of
Equality
Substitution Property of
Equality
Addition Property of
Equality
If a = b, thena – c = b – c(subtr. prop.
=)
Multiplication Property of
Equality
Division Property of
Equality
Reflexive Property of
Equality
Symmetric Property of
Equality
Transitive Property of
Equality
Substitution Property of
Equality
Addition Property of
Equality
Subtraction Property of
Equality
If a = b, thenac = bc
(mult. prop. =)
Division Property of
Equality
Reflexive Property of
Equality
Symmetric Property of
Equality
Transitive Property of
Equality
Substitution Property of
Equality
Addition Property of
Equality
Subtraction Property of
Equality
Multiplication Property of
Equality
If a=b and c0, then
(div. prop. =)
Reflexive Property of
Equality
Symmetric Property of
Equality
Transitive Property of
Equality
Substitution Property of
Equality
a bc c
Addition Property of
Equality
Subtraction Property of
Equality
Multiplication Property of
Equality
Division Property of
Equality
a = a(refl. prop.
=)
Symmetric Property of
Equality
Transitive Property of
Equality
Substitution Property of
Equality
Addition Property of
Equality
Subtraction Property of
Equality
Multiplication Property of
Equality
Division Property of
Equality
Reflexive Property of
Equality
If a = b, thenb = a
(sym. prop. =)
Transitive Property of
Equality
Substitution Property of
Equality
Addition Property of
Equality
Subtraction Property of
Equality
Multiplication Property of
Equality
Division Property of
Equality
Reflexive Property of
Equality
Symmetric Property of
Equality
If a = b and b = c, then a =
c(trans. prop.
=)
Substitution Property of
Equality
Addition Property of
Equality
Subtraction Property of
Equality
Multiplication Property of
Equality
Division Property of
Equality
Reflexive Property of
Equality
Symmetric Property of
Equality
Transitive Property of
Equality
If a = b, then b can be
substituted for a(subst. prop. =)
Example: Solve the equation 21 = 4x – 7. Write a justification for each step.
21 = 4x – 7 Given equation21 + 7 = 4x – 7 + 7 Add. prop. = 28 = 4x Simplify
7 = x Simplify x = 7 Sym. prop. =
284
4x4 Div. prop. =
Line segments with equal lengths are congruent, and angles with equal measures are also congruent. Therefore, the reflexive, symmetric, and transitive properties of equality have corresponding properties of congruence.
•Hotdog fold•Open it up and hamburger fold•Make shutters•Cut one side of shutters into two sections.
Reflexive Property of Congruence
Symmetric Property of Congruence
Transitive Propertyof Congruence
fig. A fig. A(refl. prop. )
Symmetric Property of Congruence
Transitive Propertyof Congruence
Reflexive Property of Congruence
If fig. A fig. B, then fig.B
fig.A(sym. prop.
)
Transitive Propertyof Congruence
Reflexive Property of Congruence
Symmetric Property of Congruence
If fig. A fig. B and fig. B fig. C, then figure A figure
C(trans. prop. )
Example: Write a justification for each step.
Given TA = AR Def. segments5y+6 = 2y+21 Subst. prop. =3y+6 = 21 Subtr. prop. = 3y = 15 Subtr. prop. = y = 5 Div. prop. =
RAT
5y+6 2y+21
TA AR
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