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CHAPTER 2: DEDUCTIVE
REASONING
Section 2-2: PROPERTIES
FROM ALGEBRA
PROPERTIES OF EQUALITY
1. Addition Property:
If a = b and c = d, then a + c = b + d
2. Subtraction Property:
If a = b and c = d, then a – c = b – d
3. Multiplication Property:
If a = b, then ca = cb.
PROPERTIES OF EQUALITY
4. Division Property
If a = b and c ≠ 0, then a/c = b/c
5. Substitution Property
If a = b, then either a or b may be
substituted for the other in any equation
or inequality.
PROPERTIES OF EQUALITY
6. Reflexive Property
a=a
7. Symmetric Property
If a = b, then b = a
8. Transitive Property
If a = b and b = c, then a = c.
PROPERTIES OF CONGRUENCE
1. Reflexive Property
DE ≡ DE
D≡ D
2. Symmetric Property
If DE ≡ FG, then FG ≡ DE
If D ≡ E, then E ≡ D.
PROPERTIES OF CONGRUENCE
3. Transitive Property
If DE ≡ FG and FG ≡ JK, then DE ≡ JK.
If D ≡ E and E ≡ F, then D ≡ F.
PRACTICE
Justify each step in solving the equation
3y + 4 = 2y/5
1.
2.
3.
4.
5.
3y + 4 = 2y/5
15y + 20 = 2y
13y + 20 = 0
13y = -20
y = -20/13
1.
2.
3.
4.
5.
Given
Mult. Prop. of =
Subtr. Prop. of =
Subtr. Prop. of =
Div. Prop. of =
PRACTICE
Justify each step in solving
2x + 3 = 11
1. 2x + 3 = 11
1. Given
2. 2x = 8
2. Subtraction Property
of Equality
3. x = 4
3. Division Property of
Equality
YOU TRY
Justify each step in solving
¾ x = 6 + 2x
1. ¾ x = 6 + 2x
1. Given
2. 3x = 24 + 8x
2. Mult. Prop. of =
3. -5x = 24
3. Subtr. Prop. of =
4. x = - 24/5
4. Div. Prop. of =
COMPLETING A 2-COLUMN PROOF
G
C
Given: m 1 = m 3; m 2 = m 4
1
Prove: m ABC = m DEF
1. m
m
2. m
m
1=m
2=m
1+m
3+m
3;
4
2=
4
2
A
B
H
F
4
E
3
D
1. Given
2. Add. Prop. of =
3. m 1 + m 2 = m ABC
m 3 + m 4 = m DEF
3. Angle Add. Post.
4. m ABC = m DEF
4. Substitution Prop. of
=
2 COLUMN PROOF
Given: DW = ON
Prove: DO = WN
1. DW = ON
2. DW = DO + OW;
ON = OW + WN
3.DO + OW = OW +WN
4. OW = OW
5. DO = WN
D
O
W
N
1. Given
2. Segment Add. Post.
3. Substitution Prop.
4. Reflexive Prop.
5. Subtr. Prop. of =
HOMEWORK
Classwork
• Pg. 40, Classroom Exercises 1-12 ALL
• Pg. 41-42, Written Exercises 2-10 Even