Geometry Honors

ALGEBRAIC REASONING

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.

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

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

You use deductive reasoning every time you solve an algebraic equation.You can justify every step of the solution with…A postulateA propertyA definition

Example:

Solve for x and justify each step.A

B

C

O

x(2x+10)

Given: mAOC = 139

mAOB + mBOC = mAOC

Example:

Solve for x and justify each step.

KM

N

L

(2x+40)

(4x)

Given: LM bisects KLN

LM bisects KLN

Example:

Solve for x and justify each step.

CB A

3y - 9 2yGiven: AC = 21

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.

Let’s do pg. 91 together.

#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

#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

#3

Solve for x and justify each step.

½ x – 5 = 10 Given

2(½ x – 5) = 20

x – 10 = 20

x = 30

#4

Solve for x and justify each step.

5(x + 3) = -4 Given

5x + 15 = -4

5x = -19

x = -19/5

#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

#28

Solve for x and justify each step.

K L

M2x - 5 2x Given:

KM = 35

Find the length of KL.

I

#29:

Solve for x and justify each step.G E

F

(9x-2)4x

Given: mGFI = 128

Find mEFI.

#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

HOMEWORK

Properties WSProperties WS #2

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