Transcript 2 5 Algebra Proofs

2.5 Reason Using Algebra Properties
Objectives:
Assignment:
1. To construct a logical • P.108-111: 1, 6-20
even, 21-26, 31
argument using
• Challenge Problems
algebraic properties
2. To understand the
role of proof in a
deductive system
Objective 1
You will be
able to
construct a
logical
argument
using
algebraic
properties
Exercise 1
Solve 2x +5 = 20 – 3x. Write a reason for
each step.
2x +5 = 20 – 3x
Given
5x +5 = 20
Addition Prop of =
5x = 15
x =3
Subtraction Prop of =
Division Prop of =
An Algebraic Flashback
Algebraic Properties of Equality
Let a, b, and c be real numbers.
Addition Property
Subtraction Property
Multiplication Property
Division Property
Substitution Property
Oh, Here’s One More
Distributive Property
Exercise 2
Solve −4(11x + 2) = 80. Write a reason for
each step.
Exercise 3
Solve the formula below for b1. Write a
reason for each step.
1
A  b1  b2 h
2
Even More Properties!
Even More Properties!
Any of these properties can be used as
reasons in an algebraic or geometric proof.
Exercise 4
Complete the conditional statement using the
property indicated.
1. Transitive: If 𝐽𝐷 = 𝑆𝐵 and 𝑆𝐵 = 𝑅𝐴, then
___________________.
2. Symmetric: If 𝑚∠4 = 𝑚∠2, then
___________________.
3. Substitution: If 𝑅𝐴 = 𝑆𝐵 and 𝑆𝐵 + 𝐽𝑁 = 7,
then ___________________.
2.5 Reason Using Algebra Properties
Objectives:
Assignment:
1. To construct a logical • P.108-111: 1, 6-20
even, 21-26, 31
argument using
• Challenge Problems
algebraic properties
2. To understand the
role of proof in a
deductive system