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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,

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Geometry

Geometry

2.2

Properties of Equality: POE’s

&

Properties of Congruence: POC’s


Addition poe

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

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

Multiplication POE

  • If a = b,

    then ca = cb

  • ¾ = 0.75,

    thus 100(¾) = 100(0.75)


Division poe

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

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

Distributive POE

  • a(b + c) = ab + ac

  • 5(x + 3) = 5x + 15


Reflexive

Reflexive

  • Reflexive POE

    a = a

  • Reflexive POC

    and


Symmetric

Symmetric

  • Symmetric POE

    If a = b, then b = a

  • Symmetric POC

    If , then

    If , then


Transitive property

Transitive Property

  • Transitive POE

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

  • Transitive POC

    If , and then

    If , and then


A few together

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


5 justify each step from the hw

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)


Ce 12 complete the proof given st rn it ru prove si un

.

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

CE 12) Complete the ProofGiven ST = RN; IT = RUProve: SI = UN

.

R

.

U

.

N


Homework

Homework

  • 2.2 CE #12 WE #1-11


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