1. CHAPTER 2: DEDUCTIVE REASONING
Section 2-2: PROPERTIES FROM ALGEBRA

2. PROPERTIES OF EQUALITY
Addition Property:
If a = b and c = d, then a + c = b + d
Subtraction Property:
If a = b and c = d, then a – c = b – d
3. Multiplication Property:
If a = b, then ca = cb.

3. PROPERTIES OF EQUALITY
Division Property
If a = b and c ≠ 0, then a/c = b/c
Substitution Property
If a = b, then either a or b may be substituted for the other in any equation or inequality.

4. PROPERTIES OF EQUALITY
Reflexive Property
a = a
Symmetric Property
If a = b, then b = a
Transitive Property
If a = b and b = c, then a = c.

5. PROPERTIES OF CONGRUENCE
Reflexive Property
DE ≡ DE D ≡ D
Symmetric Property
If DE ≡ FG, then FG ≡ DE
If D ≡ E, then E ≡ D.

6. PROPERTIES OF CONGRUENCE
Transitive Property
If DE ≡ FG and FG ≡ JK, then DE ≡ JK.
If D ≡ E and E ≡ F, then D ≡ F.

7. PRACTICE Justify each step in solving the equation 3y + 4 = 2y/5
Given
Mult. Prop. of =
Subtr. Prop. of =
Div. Prop. of =
3y + 4 = 2y/5
15y + 20 = 2y
13y + 20 = 0
13y = -20
y = -20/13

8. PRACTICE Justify each step in solving 2x + 3 = 11
Given
Subtraction Property of Equality
Division Property of Equality

9. YOU TRY Justify each step in solving ¾ x = 6 + 2x
Given
Mult. Prop. of =
Subtr. Prop. of =
Div. Prop. of =

10. COMPLETING A 2-COLUMN PROOF
Given: m 1 = m 3; m 2 = m 4
Prove: m ABC = m DEF H F 2 1 4 3 A B E D
m 1 = m 3;
m 2 = m 4
m m 2 =
m m 4
m m 2 = m ABC
m m 4 = m DEF
4. m ABC = m DEF
Given
Add. Prop. of =
Angle Add. Post.
Substitution Prop. of =

11. 2 COLUMN PROOF DW = ON DW = DO + OW; ON = OW + WN 3.DO + OW = OW +WN
Given: DW = ON
Prove: DO = WN D O W N
DW = ON
DW = DO + OW;
ON = OW + WN
3.DO + OW = OW +WN
4. OW = OW
5. DO = WN
Given
Segment Add. Post.
Substitution Prop.
Reflexive Prop.
Subtr. Prop. of =

12. HOMEWORK Classwork Pg. 40, Classroom Exercises 1-12 ALL
Pg , Written Exercises 2-10 Even