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Geometry
2.4 Reasoning in Algebra
Homework: P 91 #1-23, 27, 30
Properties of Equality
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If a = b, then a + c = b+ c
If a = b, then a – c = b – c
If a = b, then a  c = b  c
If a = b and c  0, then a  b
c
c
a=a
If a = b, then b = a
If a = b and b = c, then a = c
If a = b, then b can replace a in any expression
____________________ a(b+c) = ab + ac
Properties of Congruence
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AB  AB
 A  A
If AB  CD, then CD  AB
If  A  B, then  B  A
If AB  CD and CD  EF , then AB  EF
if  A  B and  B  C , then  A  C
You use deductive reasoning every time you solve an equation. You can justify each
statement that you make with a postulate, a property, or a definition.
Ex1: Name the property that justifies each statement.
a. <G  <G
b. If m<A= 10, then 2m<A = 20
c. If AB = FG, then FG = AB
d. If <A  < B and <B  <G, then <A<G
Ex2: Use the given property to complete each statement.
a. Addition property of equality: If 2x-5 = 10, then 2x = _______
b. Symmetric property of equality: If AB = YU, then ___________
c. Substitution property: If LM = 7 and EF + LM = NP, then ____________ = NP
d. Multiplication property of equality: if 1/3TR = UW, then ________________
Ex3: Justify each step used to solve 5x-12 = 32+x
1. 5x = 44 + x
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2. 4x = 44
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3. x = 11
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Ex4: Solve for n
Given XY = 42
a. XZ + ZY = XY
3n
3(n+4)
X
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b. 3(n+4) + 3n = 42 _____________________
c. 3n + 12 + 3n = 42 _____________________
d. 6n + 12 = 42
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e. 6n = 30
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f. n = 5
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Z
Y