2.4 Reasoning in Algebra 2011 September 20, 2011
2­4 Reasoning in Algebra
Objective
Justify steps in solving an equation.
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2.4 Reasoning in Algebra 2011 September 20, 2011
Warm­up:
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2.4 Reasoning in Algebra 2011 September 20, 2011
In geometry you accept postulates and properties as true. You also use them as justification to prove other statements.
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2.4 Reasoning in Algebra 2011 September 20, 2011
When solving an equation you can justify each step with a:
postulate
property
,
,
or a
definition
.
Exam
p
or Seg les: Angle A
ment Addit ddition Pos
ion Po
t
stulat ulate e
Exam
ples o
n prev
ious p
age.
Check
the ba
ck of y
our bo
o
k.
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2.4 Reasoning in Algebra 2011 September 20, 2011
Example #1: Solve for x and justify each step.
Given: m AOC = 139
B
A
x
2x + 10
O
C
Steps
Justifications
1. m AOB + m BOC = m AOC
2. x + 2x + 10 = 139
3. 3x + 10 = 139
4. 3x = 129
5. x = 43
1. Angle Addition Postulate
2. Substitution
3. Simplify
4. Subtraction Property of Equality
5. Division Property of Equality
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2.4 Reasoning in Algebra 2011 September 20, 2011
Example #2: Solve for y and justify each step.
Given: AC = 21
2y
A
Steps
1. AB + BC = AC
2. 2y + 3y ­ 9 = 21 3. 5y ­ 9 = 21
4. 5y = 30
5. y = 6
3y ­ 9
B
C
Justifications
1. Segment Addition Postulate
2. Substitution Property
3. Simplify
4. Addition Property of Equality
5. Division Property of Equality
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2.4 Reasoning in Algebra 2011 September 20, 2011
Properties of Congruence
Reflexive Property
a = a
Symmetric Property
If a = b, then b = a.
Transitive Property
If a = b and b = c, then a = c.
Substitution Property
If a = b, then b can replace a in any expression.
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2.4 Reasoning in Algebra 2011 September 20, 2011
Name the property of congruence that justifies each statement.
~
1. K = K
Reflexive Property of Congruence
~
~
~
2. If RS = TW and TW = PQ, then RS = PQ.
Transitive Property of Congruence
3. If m A = m B, then m B = m A.
Symmetric Property of Equality
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2.4 Reasoning in Algebra 2011 September 20, 2011
Homework page 105 ﴾1 ­ 23, 43 ­ 48﴿
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