Download 3x - mcomfort

Section 2.4: Reasoning with
Properties from Algebra
Geometry
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Algebraic Properties of Equality
Let a, b, and c be real numbers

Addition Property
– If a = b, then a + c = b + c

Subtraction Property
– If a = b, then a - c = b – c

Multiplication Property
– If a = b, then ac = bc

Division Property
– If a = b and c ≠ 0, then a  c = b  c
Geometry
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
Reflexive Property
– For any real number a, a = a

Symmetric Property
– If a = b, then b = a

Transitive Property
– If a = b and b = c, then a = c

Substitution Property
– If a = b, then a can be substituted for b in any
equation or expression
Geometry
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Example 1: Writing Reasons

Solve 3x + 12 = 8x -18 and write a reason for
each step
– 3x + 12 = 8x -18

(Given)
– 12 = 5x -18

(Subt. Prop of =)
– 30 = 5x

(Addition Prop of =)
– 6=x

Geometry
(Division Prop. of =)
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Properties of Equality

Reflexive
– Segment Length

For any segment AB, AB = AB
– Angle Measure

Geometry
For any angle A, mA = mA
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
Symmetric
– Segment Length

If AB = CD, then CD = AB
– Angle Measure


If mA = mB, then mB = mA
Transitive
– Segment Length

If AB = CD and CD = EF, then AB = EF
– Angle Measure

Geometry
If mA = mB and mB = mC, then
mA = mC
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Example 2: Using Prop. Of Length

AC = BD. Verify that AB = CD.
A
B
Statements
Reasons
AC = BD
Given
BC = BC
Refl. Prop of =
AC – BC = BD – BC
- Prop of =
AB + BC = AC; BC + CD = BD
Segment Add. Postulate
AB = AC – BC; CD = BD – BC
Subtraction prop of =
AB = CD
Subs. Prop of =
Geometry
C
D
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