Download G.6 Lesson 3, 2 column proofs.notebook

G.6 Lesson 3, 2 column proofs.notebook
November 21, 2016
Do Now: Find the measure of all 4 angles (not drawn to scale)
x2 ­ 15
­2x
G.6 Lesson 3 -- 2-Column Proofs
Learning Target: Today I will be able to use the 2-column proof
method of deductive reasoning to prove a statement and will do
this by building a “library of justifications” and collaboratively
proving two statements before individually completing a proof
as an exit ticket with 6 out of 8 steps justified correctly.
SOL - G.6
Homework: page 247, #9, 16, 19
G.6 Lesson 3, 2 column proofs.notebook
November 21, 2016
Step 1: Build a library of "justifications" to use when proving statements. *This library is based on what we've already learned and should grow throughout the year.
Library of Justifications
Properties of Equality
• addition
• subtraction
• multiplication
• division
Substitution Property
Transitive Property
Linear Pair Postulate
Reflexive Property
Alt Interior Angles Theorem
Symmetric Property
CPCTC
Distributive Property
Various "keyword" definitions
Angle Addition Postulate
Segment Addition Postulate
Vertical Angle Theorem
G.6 Lesson 3, 2 column proofs.notebook
November 21, 2016
Addition
Property
of equality
a+c=b+c
Subtraction
Property of
equality
Multiplication
Property of
equality
a - c = b -c
If a = b, then
axc=bxc
Division
Property of
equality
if
Properties of Equality
Reflexive
Property
Symmetric
Property
Transitive
Property
a=a
If a = b, then b = a
If a = b and b = c, then a = c
then
G.6 Lesson 3, 2 column proofs.notebook
Distributive
Property
Substitution
Property
November 21, 2016
a(b+c) = ab + ac
a(b-c) = ab - ac
If a = b, then b can replace a
in any expression.
Vertical Angles Theorem
Vertical Angles are congruent
Segment Addition Postulate
AB + BC = AC
Angle Addition Postulate
m<ABC + m<CBD = m<ABD
Linear Pair Postulate
Two linear angles are supplementary
Definitions are valid justification as well
G.6 Lesson 3, 2 column proofs.notebook
November 21, 2016
Step 2: Learn how to construct and justify a 2­column proof.
We'll start by simply solving a problem as we've always done, but....we'll add a justification for each step.
B
3x
Solve, justifying each step
2x + 6
A
WB p. 51, #2, 3
C
D
G.6 Lesson 3, 2 column proofs.notebook
November 21, 2016
Now, we'll do a full­up proof. With a proof we have a hypothesis (the "given") and a conclusion. We just have to get from p to q!
If M is the midpoint of a line segment, then x=2.
Given: M is the midpoint of AB, AM=4x+2, MB=2x+6
M
Prove: x=2
B
2x+6
A
4x+2
M is the midpoint of AB
AM=4x+2, MB=2x+6
AM = MB
4x + 2 = 2x + 6
2x + 2 = 6
2x = 4
x=2
G.6 Lesson 3, 2 column proofs.notebook
November 21, 2016
Properties of Geometric Parts
Reflexive
Property
Symmetric
Property
Transitive
Property
If
then
If
then
If
and
then
If
and
then
Do Now: List the 5 theorems/postulates available to prove two triangles congruent. Then list the two combinations that DON'T work to prove triangles congruent.
Then find the lengths of all sides of the two triangles shown.
D
A (4, 7)
2x
4x
C
B (­4, 13)
F
3x
E
G.6 Lesson 3, 2 column proofs.notebook
November 21, 2016
G.6 Lesson 3 -- 2-Column Proofs
Learning Target: Today I will be able to use the 2-column proof
method of deductive reasoning to prove a statement and will do
this by building a “library of justifications” and collaboratively
proving two statements before individually completing a proof
as an exit ticket with 6 out of 8 steps justified correctly.
SOL - G.6
Homework: page 247, #9, 16, 19
G.6 Lesson 3, 2 column proofs.notebook
November 21, 2016
,
G.6 Lesson 3, 2 column proofs.notebook
November 21, 2016
G.6 Lesson 3, 2 column proofs.notebook
November 21, 2016
G.6 Lesson 3 -- 2-Column Proofs
Learning Target: Today I will be able to use the 2-column proof
method of deductive reasoning to prove a statement and will do
this by building a “library of justifications” and collaboratively
proving two statements before individually completing a proof
as an exit ticket with 6 out of 8 steps justified correctly.
SOL - G.6
Homework: page 247, #9, 16, 19
Exit ticket: Complete the following using
2-column proof format
A
D
B
Given: ∠ABC and ∠DBE are vertical angles
3x+1
6x‐2
And m∠ABC=3x+1 and m∠DBE=6x‐2
Prove: x = 1
Homework: p.247, #9, 16, 19
c
E
G.6 Lesson 3, 2 column proofs.notebook
November 21, 2016