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SB En Geom 2­4 Completed.notebook
September 12, 2012
Lesson 2.4 Reasoning with Properties from Algebra
Algebraic Properties
Addition Prop. If a = b, then a + c = b + c
Subtraction Prop. If a = b, then a ­ c = b ­ c
Multiplication Prop. If a = b, then ac = bc.
Division Prop.If a = b and c ≠ 0, then a÷c = b÷c
Reflexive Prop.For any real number a, a = a.
Symmetric Prop. If a = b, then b = a.
Transitive Prop.If a = b and b = c, then a = c.
Sep 6­2:06 PM
Substitution Prop. If a = b, then a can be substituted for b in
any equation or expression.
The Distributive Property
a ( b + c ) = ab + ac
Sep 8­3:20 PM
1
SB En Geom 2­4 Completed.notebook
September 12, 2012
Expl 1. Justify each step in solving.
B
A
x
Solve for x and justify each step.
Given: m<AOC = 139
(2x + 10)
O
C
StatementsReasons
m<AOB + m<BOC = m<AOC
x + 2x + 10 = 139
3x + 10 = 139
3x = 129
x = 43
Sep 8­3:25 PM
M
Ckpt 1. Fill in each missing reason.
(2x+40)
Given: LM bisects <KLN.
K
L
4x
N
StatementsReasons
LM bisects <KLN. Given
m<MLN = m<KLM Defn of angle bisector
4x = 2x + 40
2x = 40
x = 20
Sep 8­3:29 PM
2
SB En Geom 2­4 Completed.notebook
September 12, 2012
Expl 2. Solve for y and justify each step.
3y - 9
2y
Given AC = 21
A
B
C
StatementsReasons
AB + BC = AC
2y + ( 3y ­ 9 ) = 21
5y ­ 9 = 21
5y = 30
y = 6
Sep 8­3:33 PM
Ckpt 2. Find AB and BC by substituting y = 6 in the expressions in the diagram above. Check that AB + BC = 21.
3y - 9
2y
A
B
C
Sep 8­3:36 PM
3
SB En Geom 2­4 Completed.notebook
September 12, 2012
Properties of Congruence
ReflexiveAB ≅ AB
<A ≅ <A
Symmetric If AB ≅ CD, then CD ≅ AB.
If <A ≅ <B, then <B ≅ <A.
Transitive
If AB ≅ CD and CD ≅ EF, then AB ≅ EF.
if m<A ≅ m<B and m<B ≅ m<C, then m<A ≅ m<C.
Sep 6­2:22 PM
Expl 3. Name the property of equality or congruence that justifies each statement.
a. <K ≅ <K
b. If 2x ­ 8 = 10, then 2x = 18.
c. If RS ≅ TW and TW ≅ PQ, then RS ≅ PQ.
d. If m<A = m<B, then m<B = m<A.
3
a. XY ≅ XY
b. If m<A = 45 and 45 = m<B, then m<A = m<B.
Sep 8­3:38 PM
4
SB En Geom 2­4 Completed.notebook
September 12, 2012
Homework
Lesson 2­4
1­24, 28, 30, 38­41
Sep 6­2:41 PM
5
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