Download Warm-Up 9/5/2014

Warm-Up 9/5/2014
1. Find the measure of MN if N is between M and
P, MP = 6x - 2, MN = 4x, and NP = 16.
2. State which postulate justifies each statement:
• If D is in the interior of ∠ABC, then
m∠ABD + m ∠DBC = ∠ABC
• If M is between X and Y, then
XM + MY = XY
Chapter 2 – Logic, Postulates,
and Proofs
Tue
9/2 – 2.2 – Conditional Statements
Thu
9/4 – 2.4, 2.5, & 2.6 – Postulates, Algebra, and
Proving Statements about Segments and Angles
Fri
9/5 – More 2.6 – Proving Statements about Segments and
Angles
Mon
9/8 – 2.7 – Proving Angle Pair Relationships
Tue
9/9 – Review of Chapter 2
Thu
9/11 – Chapter 2 Quiz, Start on Ch. 3
Proof
• A series of logical statements that lead us to a
final place.
• Each Statement has a supporting Reason
• Reasons can be, Definitions, Properties,
Postulates or Theorems
Key Vocabulary
• Theorem
– A statement that can be proven.
How is this different from a postulate?
• Angle Bisector
– A ray, line, or line segment that divides an angle
into two angles that are congruent.
Congruence Theorems
Congruence Theorems
• Congruence of Segments Theorem:
Segment congruence is Reflexive, Symmetric, and
Transitive.
Congruence Theorems
• Congruence of Angles Theorem:
Angle congruence is Reflexive, Symmetric, and
Transitive.
Proofs with Algebra
• Solve:
2x + 5 = 20 – 3x
Statement
Reason
Write your steps here
Support each Statement with a
Postulate (from yesterday)
Proofs with Algebra
• Solve:
2x + 5 = 20 – 3x
Statement
2x + 5 = 20 – 3x
-5 -5
2x
= 15 – 3x
+ 3x
+ 3x
5x =
15
5 x / 5 = 15 / 5
x=3
Reason
1. Given
2. Subtraction Prop. Of Equality
3. Addition Prop. Of Equality
4. Division Prop. Of Equality
5. Solution
Proofs with Algebra
• Solve:
2x + 5 = 20 – 3x
Statement
2x + 5 = 20 – 3x
+ 3x
+ 3x
5x + 5 =
20
-5
-5
5x
= 15
5 x / 5 = 15 / 5
x=3
Reason
1. Given
2. Addition Prop. Of Equality
3. Subtraction Prop. Of Equality
4. Division Prop. Of Equality
5. Solution
Proofs with Algebra
• Solve:
2x + 5 = 20 – 3x
Statement
2x + 5 = 20 – 3x
+ 3x
+ 3x
5x + 5 = 20
5x/5 + 5/5 = 20/5
x + 1 = 4
-1
-1
x
= 3
Reason
1. Given
2. Addition Prop. Of Equality
3. Division Prop. Of Equality
4. Subtraction Prop. Of Equality
5. Solution
Proofs
• There can be many different routes to the
same goal!
Proofs – My Approach
1. Identify what is Given
•
The first line (or two) in your proof will almost always be
your Given
2. Identify your Goal (i.e. what they want you to prove)
3. Do a rough draft, mapping how you think you can
get to your goal
4. Figure out how you can support your steps using
Definitions, Properties, Postulates, and Theorems
5. Convert your draft into formal language
Proofs with Geometry
• For now, you will likely be given a proof with
pieces missing – either Statements or Reasons
Exit Slip
1. How do you feel this course is going?
On a scale of 1-10, is it way too easy (1), way too hard (10), or
somewhere in between? Give me a number and then write a few
sentences of explanation.
2. Can you think of anything I can/should do differently
that will help YOU in this course?
Any and all suggestions are welcome.
--
HOMEWORK: pg. 116-118, #3-11, 16, 17, 22, #30 is
optional but is a good challenge