Download Section 2.4 Day 1 Reasoning with Properties From Algebra

Week 7
09.28.11
Warm Up
1) What is the postulate?
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A
m∠ADB + m∠BDC = m∠ADC
2) If ∠ 4 and ∠ 5 are a linear pair
and ∠ 4 = 79⁰. What is m ∠ 5?
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D
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Geometry
2.4 Day 1
Properties
of Equality
I will use the properties of algebra to write
reasons for steps in solving equations.
Addition:
If a = b then a + c = b + c
Subtraction:
If a = b then a - c = b - c
Properties
of Equality
Multiplication:
Division:
If a = b then ac = bc
If a = b then
a
b
c = c
Properties
of Equality
Substitution:
Distributive:
If a = b then b can replace a.
If a( b + c ) = ab + ac
Ex 1
Solve and
give reasons:
55z – 3( 9z + 12 ) = -64
Step
Reason
55z – 3( 9z + 12 ) = -64
Given
55z - 27z - 36 = -64
Distributive property
28z - 36 = -64
Simplify
28z = -28
Addition property
of equality
z = -1
Division property
of equality
Properties
of equality
for
Segment
length
Segment Length
Reflexive:
AB = AB
Symmetric:
If AB = CD, then CD = AB
Transitive:
If AB = CD, and CD = EF,
then AB = EF.
Properties
of equality
for angle
measure
Angle Measure
Reflexive:
m∠A = m∠A
Symmetric:
If m∠A = m∠B,
then m∠B = m∠A
Transitive:
If m∠A = m∠B,
and m∠B = m∠C
then m∠A = m∠C
Ex 2
m ∠ 1 + m ∠ 2 = 132⁰
m ∠ 2 = 105⁰
2
show that m ∠ 1 = 27⁰
Step
m ∠ 1 + m ∠ 2 = 132⁰
m ∠ 2 = 105⁰
Reason
Given
Given
1
Ex 1
m ∠ 1 + m ∠ 2 = 132⁰
m ∠ 2 = 105⁰
2
show that m ∠ 1 = 27⁰
Step
m ∠ 1 + m ∠ 2 = 132⁰
m ∠ 2 = 105⁰
Reason
Given
Given
1
Ex 3
m ∠ 1 + m ∠ 2 = 132⁰
m ∠ 2 = 105⁰
2
1
show that m ∠ 1 = 27⁰
Step
Reason
m ∠ 1 + m ∠ 2 = 132⁰
Given
m ∠ 2 = 105⁰
Given
m ∠ 1 + 105⁰ = 132⁰
m ∠ 1 = 27⁰
Substitution property of Eq.
Subtraction property of Eq.
Do: 1
What is the property when 5x + 7y = 58
and x = 27
5x + 7y = 58
5( 27 ) + 7y = 58
Assignment:
Textbook Page 99, 10 - 27 All
given
?