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# Geometry - PowerPoint PPT Presentation

Geometry. 2.2 Properties of Equality: POE’s &amp; 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,

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### 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,

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
• Addition 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

4) Add. 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

2) Segment Add. Post.

3) Subst. POE

4) Given

5) Subtr. POE

.

R

.

U

.

N

Homework
• 2.2 CE #12 WE #1-11