1. Properties from Algebra
Section 2-2:
Properties from Algebra

2. a + c = b + d Ex: If x = 12, then x + 2 = 14.
Properties of Equality
Addition Property
If a = b and c = d, then _________________________.
Subtraction Property
If a = b and c = d, then __________________________.
Multiplication Property
If a = b, then _________________________________.
Division Property
If a = b and c ≠ 0, then ________________________.
a + c = b + d
Ex: If x = 12, then x + 2 = 14.
If x – 3 = 7, then x = 10.
a – c = b – d
Ex: If x + 2 = 9, then x = 7.
ca = cb
Ex: If 𝑥 3 = 9, then x = 27.
𝑎 𝑐 = 𝑏 𝑐
Ex: If 4x = 28, then x = 7.

3. Substitution Property If a = b, then either a or b may be ____________ for the other in any equation (or inequality).
substituted
Ex: If m∠A = 30° and m∠A = m∠C, then m∠C = 30°.
Ex: If 2x + 3 = y and x = 5, then 13 = y.
Ex: If x = y and z = y, then x = z.

4. Reflexive Property
a = _____
Symmetric Property
If a = b, then ____________________.
Transitive Property
If a = b and b = c, then _____________. a
Ex: If m∠A, then m∠A.
b = a
Ex: If AB = CD, then CD = AB.
a = c
Ex: If m∠A = m∠B and m∠B = m∠C, then m∠A = m∠C.

5. 𝐷𝐸 ∠D 𝐹𝐺 ≅ 𝐷𝐸 ∠E ≅ ∠D 𝐷𝐸 ≅ 𝐽𝐾 ∠D ≅ ∠F
Properties of Congruence Reflexive Property 𝐷𝐸 ≅ ________ ∠D ≅ _________ Symmetric Property If 𝐷𝐸 ≅ 𝐹𝐺 , then _____________________________. If ∠D ≅ ∠E, then ______________________________. Transitive Property If 𝐷𝐸 ≅ 𝐹𝐺 and 𝐹𝐺 ≅ 𝐽𝐾 , then ­­­_______________. If ∠D ≅∠E and ∠E ≅∠F, then _________________. 𝐷𝐸 ∠D
𝐹𝐺 ≅ 𝐷𝐸
∠E ≅ ∠D
𝐷𝐸 ≅ 𝐽𝐾
∠D ≅ ∠F

6. Properties of Real Numbers
Commutative Property
a + b = __________, ab = _______
Associative Property
a + (b + c) = _________, a(bc) = ________
Distributive Property
a(b + c) = __________
b + a ba
(a + b) + c
(ab)c
ab + ac

7. Examples:
Justify each step with a “Property from Algebra.”
Follow the example below:
Given: 4x – 5 = –2
Prove: x = 3 4
Statements Reasons
1. 4x – 5 = – Given
2. 4x = Addition Property of Equality
3. x = Division Property of Equality

8. Multiplication Property of Equality
1. Given: 3𝑎 2 = 6 5
Prove: a = 4 5
Statements Reasons
1. 3𝑎 2 = Given
2. 3a =
3. a =
Multiplication Property of Equality
Division Property of Equality

9. 2. Given: 𝑧+7 3 = –11 Prove: z = –40 Statements Reasons 1
2. Given: 𝑧+7 3 = –11 Prove: z = –40 Statements Reasons 1. 𝑧+7 3 = –11 1. Given 2. z + 7 = – z = –40 3.
Multiplication Property of Equality
Subtraction Property of Equality

10. Addition Property of Equality
3. Given: 15y + 7 = 12 – 20y Prove: y = 1 7 Statements Reasons 1. 15y + 7 = 12 – 20y 1. Given 2. 35y + 7 = y = y =
Addition Property of Equality
Subtraction Property of Equality
Division Property of Equality

11. Multiplication Property of Equality
4. Given: x – 2 = 2𝑥+8 5 Prove: x = 6 Statements Reasons 1. x – 2 = 2𝑥 Given 2. 5(x – 2) = 2x x – 10 = 2x x – 10 = x = x = 6 6.
Multiplication Property of Equality
Distributive Property
Subtraction Property of Equality
Addition Property of Equality
Division Property of Equality

12. Substitution Property Practice
  1. a = b + c Given
d = e + f
2. a = d Given
3. ____________ 3. Substitution
b + c = e + f

13. II.
1. a = b + c Given
d = e + f
2. b + c = e + f Given
3. _____________ 3. Substitution
a = d

14. (Diagram is for III. And IV.) III. 1. DF = AC 1. Given
   
1. DF = AC 1. Given
2. DE + EF = ____ 2. ____________
AB + BC = ____ ____________
3. ____________ 3. Substitution • • • D E F • • • A B C DF
Segment AC
Addition Post.
DE + EF = AB + BC

15. IV. 1. DE + EF = AB + BC 1. Given 2. DE + EF = _____ 2
IV. 1. DE + EF = AB + BC 1. Given 2. DE + EF = _____ 2. ______________ AB + BC = _____ ______________ 3. _____________ 3. Substitution DF
Segment AC
Addition Post.
DF = AC

16. m∠WOY = m∠1 + m∠2 2. _____________ m∠XOZ = m∠3 + m∠2 _____________ V.
1. ∠WOY  ∠XOZ 1. Given
m∠WOY = m∠1 + m∠2 2. _____________
m∠XOZ = m∠3 + m∠ _____________
3. ________________ 3. Substitution
________________
Angle
Addition Post.
m∠1 + m∠2 =
m∠3 + m∠2 W • X • Y • 1 2 3 • • O Z

17. CLASSWORK: page 41 #1-8 all