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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

- 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

- If a = b,
then ca = cb

- ¾ = 0.75,
thus 100(¾) = 100(0.75)

- If a = b and c 0,
then a/c = b/c

- 8 = 8.0 and 2 0,
thus 8/2 = 8.0/2

- 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

- a(b + c) = ab + ac
- 5(x + 3) = 5x + 15

- Reflexive POE
a = a

- Reflexive POC
and

- Symmetric POE
If a = b, then b = a

- Symmetric POC
If , then

If , then

- Transitive POE
If a = b, and b = c, then a = c

- Transitive POC
If , and then

If , and then

- 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

.

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

- 2.2 CE #12 WE #1-11