Download Geometry 2.5 Notes Algebraic Properties

Chapter 2
Section 2.5
Reasoning With Properties of
Algebra
Algebraic Properties of Equality
• Let a, b,c be real numbers
– Addition property of equality
• If a = b, then a + c = b + c
– Subtraction property of equality
• If a = b, then a - c = b – c
– Multiplication property of equality
• If a = b, then ac = bc
– Division property of equality
• If a = b and c  0, then a  c = b  c
Algebraic Properties of Equality
• Let a, b,c be real numbers
– Reflexive property of equality
• For any real number a, a = a
– Symmetric property of equality
• If a = b, then b = a
– Transitive property of equality
• If a = b and b = c, then a = c
– Substitution property of equality
• If a = b, then a can be substituted for b in any
equation or expression
Use the property to complete the
statement
1. Reflexive property of equality: mT = m T
KL = RW
MN = RW, then _____
2. Transitive property: If KL = MN and _____
17 + 5
3. Addition property of equality: If x = 5, then 17 + x = ______
RL = BC
4. Symmetric property of equality: If BC = RL, then ______
5. Substitution property of equality:
mB = 45 + 90 = 135
If mA = 45 and mB = mA + 90 then____
6. Multiplication property of equality: If mA = 45, then _____
1
(mA) = 15
3
Complete the argument, giving a
reason for each step
Distributive Property
Addition Property of =
Subtraction Property of =
Complete the argument, giving a
reason for each step
Addition Property of =
Addition Property of =
Division Property of =
Complete the argument, giving a
reason for each step
Segment Addition Postulate
Substitution prop of =
Substitution property of =
Complete the argument, giving a
reason for each step
Given
a. Reflexive prop of =
b. Addition property of =
c. Angle Addition postulate
d. Angle Addition postulate
e. Substitution property of =
Complete the argument, giving a
reason for each step
Given
a. Definition  lines
b. Definition  lines
c. Substitution property of =
HW #20
Pg. 108-109 #1-29