2.4 Reasoning with Properties from Algebra Use properties of Algebra.
Chapter 2 Lesson 4 Objective: To connect reasoning in algebra to geometry.
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Transcript of Chapter 2 Lesson 4 Objective: To connect reasoning in algebra to geometry.
Chapter 2 Chapter 2 Lesson 4Lesson 4Objective: To
connect reasoning in algebra to geometry.
Properties of Properties of EqualityEquality
•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 a•c = b•c
•Division Property If a=b and c≠0, then a/c = b/c
•Reflexive Property 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 b can replace a in any expression
••
B
O C
Angle Addition Angle Addition PostulatePostulate
The Distributive The Distributive PropertyProperty
a(b+c) = ab + ac
If point B is in the interior of AOC, then m AOB + m BOC = m AOC.
A •
Solve for x and justify each step.
Given: Given: m AOC = 139
Example 1:Example 1:
• ••
AB
CO
x°(2x + 10)°
m AOB + m BOC = m AOC Angle Addition Postulate
x + 2x + 10 = 139 Substitution Property 3x + 10 = 139 Simplify 3x = 129 Subtraction Property
of = x = 43 Division Property of =
Example 2:Example 2:Justify each step used to solve 5x – 12 = 32 + x5x – 12 = 32 + x for x.
5x = 44 + x
4x = 44
X = 11
Addition Property of Equality
Subtraction Property of Equality
Division Property of Equality
• ••
KM
NL
(2x + 40)°4x°
Example 3:Example 3:Fill in each missing reason.
LM bisects KLN Given
m MLN = m KLM Definition of angle bisector
4x = 2x + 40 _____________________
2x = 40 _____________________
x = 20 _____________________
Substitution Prop.
Subtraction Prop. of Equality
Division Prop. Of Equality
Example 4:Example 4:Solve for yy and justify each step.
2y 3y-9
A B CGiven: AC = 21
AB + BC = AC
2y + (3y – 9) = 21
5y – 9 = 21
5y = 30
Y = 6
Segment Addition Postulate
Substitution Property
Simplify
Addition Property of Equality
Division Property of Equality
Properties of Properties of CongruenceCongruence
Reflexive Property AB AB
A A
Symmetric Property If AB CD, then CD AB
If A B, then B A
Transitive Property If AB CD and CD EF, then AB EF
If A B and B C, then A C.
Example 5:Example 5:Name the property of equality or congruence that justifies each statement.
a. K K Reflexive Property of Congruence
b. If 2x – 8 = 10, then 2x = 18
Addition Property of Equality
c. If x = y and y + 4 = 3x, then x + 4 = 3x.
Substitution Property of Equality
d. If RS TW and TW PQ, then RS PQ. Transitive Property of Congruence
AssignmentAssignment
Page 91-93Page 91-93
#1-30#1-30