Geometry 2 2 Properties of Equality POEs Properties

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) = 5 x + 15

Reflexive POE a=a Reflexive POC and

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

Transitive Property Transitive POE If a = b, and b = c, then a = c Transitive POC If , and then

A Few Together Please turn to page 40. Let’s try #1 -10. 1) Reflexive POE 2) Transitive POE 3) Symmetric POE 4) Subtraction POE 5) Division POE 6) Multiplication POE 7) Distributive POE 8) Addition POE 9) Substition POE 10) Transitive POE

5) Justify each step(from the HW) 1) 2/3 B = 8 – 2 B 1) Given 2) 2 B = 3(8 – 2 B) 2) Mult. POE 3) 2 B = 24 – 6 B 3) Distr. POE 4) 8 B = 24 4) Add. POE 5) B = 3 5) Div. POE

CE 12) Complete the Proof Given ST = RN; IT = RU Prove: SI = UN . S. . . R U I 1) ST = RN 1) Given 2) ST = SI + IT RN = RU + UN 3) SI + IT = RU + UN 2) Segment Add. Post. 4) 4) Given 5) SI IT = RU = UN 3) Subst. POE 5) Subtr. POE . T. N

Homework 2. 2 CE #12 WE #1 -11