Download 5 Algebra Proof and Properties

5 Algebra Proof and Properties
Problems of the day
Use the diagram to write an example of Postulate 7.
True or False
GH lies in plane M.
The intersection of planes M and N is points B, E and H.
2.5 Algebra Proofs
The students will be able to solve an equations and justify each step with the appropriate property. Algebra proofs are solving equations, while providing justification for each step­all in a two­column format. Not only do you perform operations on one or both sides of an equation, you also state the property/rule that allows you to perform that operation. If you hate to show work, this is NOT your section!
Algebra Properties of Equality
Addition Property
If a = b, then a + c = b + c
Subtraction Property
If a = b, then a ­ c = b ­ c
Multiplication Property
If a = b, then ac = bc
Division Property
If a = b, then a / c = b / c
Substitution Property
If a = b, then a can be substituted for b
Distributive Property
a(b + c) = ab + ac
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5 Algebra Proof and Properties
Example: Name the property that justifies the statement.
1) If x + 3 = 17, then x = 14
2) If 3x ­ 3 + 4x = 7, then 7x ­ 3 = 7
3) If 7x = 42, then x = 6
4) 2(x + 4) = 2x + 8
Solve the equations. Write the reasons for each step.
Write a 2 column proof
1. Given:
3x + 12 = 27
Prove:
x = 5
Statement
Reason
2. Given: 4x ­ 3(x + 2) = 16
Prove: x = 22
Statement
Reason
3. Given: x+y =9
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Prove: y = ­x + 27
Statement
Reason
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5 Algebra Proof and Properties
Geometry/Algebra Proofs
Reflexive Property of Equality
Real numbers
Segments
Angles
a = a
AB = AB
m<A = m<A
Symmetric Property of Equality
Real numbers
Segments
Angles
If a = b then b = a
If AB = CD, then CD = AB
If m<A = m<B, then m<B = m<A
Transitive Property of Equality
Real numbers
Segments
Angles
If a = b and b = c, then a = c
If AB = CD and CD = EF, then AB = EF
If m<A = m<B and m<B = m<C, then m<A = m<C
Use the properties to complete the statement.
1. Symmetric Property of Equality: If m<1 = m<2, then
2. Addition Property of Equality: If AB = CD, then
______ + ED = ______ + ED
3. Transitive Property of Equality: If m<1 = m<2 and m<2 = m<3, then Name the property.
If GH = JK, then JK = GH.
If r = s, and s = 44, then r = 44
m<N = m<N
Use the properties of equality
A
B
C
D E
F
Show that CF = AD
Equation
AB = BC = AC = AB + BC
DF = DF = BC + AB
DF = DF + CD = + CD
= DF + CD
= AC + CD
=
Reason
Given
Given
Segment Addition Postulate
Property of Equality
Property of Equality
Property of Equality
Segment Addition Postulate
Segment Addition Postulate
Substitution Property of Equality
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