Warm-Up 9/5/ Find the measure of MN if N is between M and P, MP = 6x - 2, MN = 4x, and NP = 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 Mon9/8 – 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 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 StatementReason Write your steps hereSupport each Statement with a Postulate (from yesterday)

Proofs with Algebra Solve: 2x + 5 = 20 – 3x StatementReason 2x + 5 = 20 – 3x x = 15 – 3x + 3x + 3x 5 x = 15 5 x / 5 = 15 / 5 x = 3 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 StatementReason 2x + 5 = 20 – 3x + 3x + 3x 5x + 5 = x = 15 5 x / 5 = 15 / 5 x = 3 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 StatementReason 2x + 5 = 20 – 3x + 3x + 3x 5x + 5 = 20 5x/5 + 5/5 = 20/5 x + 1 = 4 x = 3 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 , #3-11, 16, 17, 22, #30 is optional but is a good challenge