algebraic reasoning
DESCRIPTION
Algebraic Reasoning. Geometry Honors. Algebra Logi c. 1. It is a four-digit number. 2. It is greater than 4000. 3. The sum of its hundreds digit and its ones digit is 9. 4. Twice its tens digit is 2 more than its thousands digit. - PowerPoint PPT PresentationTRANSCRIPT
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Geometry Honors
ALGEBRAIC REASONING
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Algebra Logic
3. The sum of its hundreds digit and its ones digit is 9.
4. Twice its tens digit is 2 more than its thousands digit.
5. The sum of one-fifth of its hundreds digit and two thirds of its ones digit is 6.
6. Its tens digit is 1 less than its thousands digit.7. The product of its hundreds digit and its ones
digit is 0.8. It is not an even number.9. It is less than 5000.10. Its tens digit is 3.
1. It is a four-digit number.2. It is greater than 4000.
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Properties
Property ExampleAddition If a=b, then a+c=b+c.Subtraction If a=b, then a-c=b-c.Multiplication
If a=b, then ac=bc.
Division If a=b and c0, then a/c=
b/c
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Properties
Property ExampleReflexive a = aSymmetric If a=b, then b=a.Transitive If a=b and b=c, then a=c.Substitution If a=b, then b can replace
a in any expression.
Distributive a(b+c) = ab+ ac
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You use deductive reasoning every time you solve an algebraic equation.You can justify every step of the solution with…A postulateA propertyA definition
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Example:
Solve for x and justify each step.A
B
C
O
x(2x+10)
Given: mAOC = 139
mAOB + mBOC = mAOC
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Example:
Solve for x and justify each step.
KM
N
L
(2x+40)
(4x)
Given: LM bisects KLN
LM bisects KLN
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Example:
Solve for x and justify each step.
CB A
3y - 9 2yGiven: AC = 21
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Properties of Congruence
Property ExampleReflexive AB AB
A A
Symmetric If AB CD, then CD AB.If A B, then B A.
Transitive If AB CD and CD EF, then AB EF.If A B and B C, then A C.
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Let’s do pg. 91 together.
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#1
Solve for x and justify each step.E
C F
D
x (3x+20)
mCDE + mEDF = 180
x + (3x+20) = 180
4x + 20 = 180
4x = 160
x = 40
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#2
Solve for n and justify each step.
X Z
Y3(n + 4) 3n Given:
XY = 42
XZ + ZY = XY
3(n+4) + 3n = 42
3n + 12 + 3n = 42
6n + 12 = 42
6n = 30
n = 5
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#3
Solve for x and justify each step.
½ x – 5 = 10 Given
2(½ x – 5) = 20
x – 10 = 20
x = 30
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#4
Solve for x and justify each step.
5(x + 3) = -4 Given
5x + 15 = -4
5x = -19
x = -19/5
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#27
Solve for x and justify each step.
A C
D4x 2x + 12
Given: C is the midpoint of AD
C is the midpoint of AD
AC = CD
4x = 2x + 12
2x = 12
x = 6
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#28
Solve for x and justify each step.
K L
M2x - 5 2x Given:
KM = 35
Find the length of KL.
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I
#29:
Solve for x and justify each step.G E
F
(9x-2)4x
Given: mGFI = 128
Find mEFI.
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#30:
Solve for n and justify each step.A
B
(6n+1)
(4n+19)
Given: BC bisects ABD
BC bisects ABD mABC = mCBD 6n + 1 = 4n + 19 2n = 18 n = 9
C
D
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HOMEWORK
Properties WSProperties WS #2
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