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Geometry
2.5 – Reason Using Properties from Algebra
Learning Target: By the end of today’s lesson we will successfully be able to reason using properties of algebra.
Algebraic Properties of Equality:
Let a, b, and c be real numbers.
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Addition Property: If a = b, then ________________________________________________________________
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Subtraction Property: If a = b, then ______________________________________________________________
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Multiplication Property: If a = b, then ____________________________________________________________
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Division Property: If a = b and c  0. then__________________________________________________________
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Substitution Property: If a = b, then _____________________________________________________________
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Distributive Property: If a(b + c), then ___________________________________________________________
1) Solve 3x + 8 = – 4x – 34. Write a reason for each step.
Statements:
1.
Reasons:
1.
2.
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3.
3.
4.
4.
2) Solve 60 = – 3(8x – 4). Write a reason for each step.
Statements:
1.
Reasons:
1.
2.
2.
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4.
3) Solve 4(5  x) =  2x. Write a reason for each step.
Statements:
Reasons:
4) 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.
Statements:
Reasons:
Reflexive Properties of Equality:
- Real Numbers: For any real number a, __________________
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Segment Length: For any segment AB, __________________
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Angle Measure: For any angle A, ______________________
Symmetric Property of Equality:
- Real Numbers: For any real numbers a and b, if a = b, then ___________________
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Segment Length: For any segments AB and CD, if AB = BC, then _____________________
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Angle Measure: For any angles A and B, if mA = mB, then ________________________
Transitive Properties of Equality:
- Real Numbers: For any real numbers a, b, and c, if a = b and b = c, then _______________
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Segment Length: For any segments AB ,CD, and EF if AB = CD , and CD = EF, then______________
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Angle Measure: For any angles A, B, and C, if mA = mB and mB = mC, then _______________
5) Given m < AOC = 145°, Prove x = 35
Statements:
Reasons:
6) Name the property of equality that the statement illustrates.
a) If GH = JK, then JK = GH.
b) If r = s, and s = 44, then r = 44.
c) mN = mN