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Name:_______________________
Notes 2.5 Reason Using Properties from Algebra
ALGEBRAIC PROPERTIES OF EQUALITY
Let a, b, and c be real numbers.
Addition Property
Subtraction Property
Multiplication Property
Division Property
Substitution Property
Distributive Property
If a = b, then ____________________________.
If a = b, then ____________________________.
If a = b, then ____________________________.
If a = b and c  0. then____________________.
If a = b, then ____________________________
_______________________________________
a(b + c) =_________, where a, b, and c are real numbers.
Example 1: Write reasons for each step
Solve 2x + 5 = 20  3x. Write a reason for each step.
Equation
2x + 5 = 20 – 3x
2x + 5 - __ = 20  3x - ___
Reason
Given
Subtraction Property of Equality
Example 2: Use the Distributive Property
Solve 4(11x + 2) = 80. Write a reason for each step.
Equation:
Reason:
Solve x  5 = 7 + 2x.
Write a reason for each step.
Solve 4(5x) = 2x.
Write a reason for each step.
Equation:
Reason:
Equation:
Reason:
Example 3: Use properties in the real world
Speed A motorist travels 5 miles per hour slower than the speed limit s for 3.5 hours. The distance traveled d
can be determined by the formula d = 3.5(s  5). Solve for s.
Equation
Reason
d = 3.5(s5)
Given
REFLEXIVE PROPERTY OF EQUALITY
Real Numbers
For any real number a, ______.
Segment Length
For any segment AB, __________.
Angle Measure
For any angle A, _________________.
SYMMETRIC PROPERTY OF EQUALITY
Real Numbers
Segment Length
Angle Measure
For any real numbers a and b, if a = b,
then ________.
For any segments AB and CD, if AB =
CD, then__________.
For any angles A and B, and if mA =
mB then ________.
TRANSITIVE PROPERTY OF EQUALITY
For any real numbers a, b, and c, if a = b
Real Numbers
and b= c, then ___________.
For any segments AB ,CD, and EF if AB
Segment Length
= CD ,and CD = EF, then__________.
Angle Measure
For any angles A, B, and C, if mA =
mB and mB = mC, then ________.
Example 4: Use properties of equality
Show that CF = AD.
Equation
AB = _____
BC = _____
AC = AB + BC
Reason
Given
Given
___________________________
____________________
DF = _____ + _____
DF = BC + AB
DF = ______
DF + CD = ________ + CD
_____ = _____
Segment Addition Postulate
_____________ Property of Equality
_____________ Property of Equality
_____________ Property of Equality
Substitution Property of Equality
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