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# Geometry PowerPoint PPT Presentation

Geometry. 2.2 Properties of Equality: POE’s & Properties of Congruence: POC’s. Addition POE. If a = b and c = d, then a + c = b + d ½ = 0.5 and 2 = 2.0, thus ½ + 2 = 0.5 + 2.0. Subtraction POE. If a = b and c = d, then a - c = b - d 10 = 10.0 and ¼ = 0.25,

Geometry

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## Geometry

2.2

Properties of Equality: POE’s

&

Properties of Congruence: POC’s

• If a = b and c = d,

then a + c = b + d

• ½ = 0.5 and 2 = 2.0,

thus ½ + 2 = 0.5 + 2.0

### Subtraction POE

• If a = b and c = d,

then a - c = b - d

• 10 = 10.0 and ¼ = 0.25,

thus 10 – 1/4 = 10.0 – 0.25

### Multiplication POE

• If a = b,

then ca = cb

• ¾ = 0.75,

thus 100(¾) = 100(0.75)

### Division POE

• If a = b and c 0,

then a/c = b/c

• 8 = 8.0 and 2 0,

thus 8/2 = 8.0/2

### Substitution POE

• If a = b,

then either a or b may be substituted for the other in an equation or inequality.

• If x = 5,

then (x) + 10 = (5) + 10

### Distributive POE

• a(b + c) = ab + ac

• 5(x + 3) = 5x + 15

### Reflexive

• Reflexive POE

a = a

• Reflexive POC

and

### Symmetric

• Symmetric POE

If a = b, then b = a

• Symmetric POC

If , then

If , then

### Transitive Property

• Transitive POE

If a = b, and b = c, then a = c

• Transitive POC

If , and then

If , and then

### A Few Together

• Please turn to page 40. Let’s try #1-10.

• Reflexive POE

• Transitive POE

• Symmetric POE

• Subtraction POE

• Division POE

• Multiplication POE

• Distributive POE

• Substition POE

• Transitive POE

1) 2/3B = 8 – 2B

2) 2B = 3(8 – 2B)

3) 2B = 24 – 6B

4) 8B = 24

5) B = 3

1) Given

2) Mult. POE

3) Distr. POE

5) Div. POE

### 5) Justify each step(from the HW)

.

S

.

I

.

T

1) ST = RN

2) ST = SI + IT

RN = RU + UN

3) SI + IT = RU + UN

4) IT = RU

5) SI = UN

1) Given

3) Subst. POE

4) Given

5) Subtr. POE

.

R

.

U

.

N

### Homework

• 2.2 CE #12 WE #1-11