Bell Work 10/3/11 1) Solve for the following and provide a reason for each step in the process 4(x – 5) = x + 4 2) Use your notes to give the property that justifies each statement A) If m ∠ 1 = m ∠ 2, then m ∠ 2 = m ∠ 1 B) m ∠ 2 = m ∠ 2 C) If EF = GH and GH = IJ, then EF = IJ D) If EF = 8 and EF = GH, then 8 = GH 3) Determine if the argument uses the Law of Detachment, the Law of Syllogism, or neither If I go to the movie, then I’ll eat popcorn. If I eat popcorn, then I’ll enjoy the movie 4) Determine if the argument uses the Law of Detachment, the Law of Syllogism, or neither If I miss my bus, then I’ll be late for school. I miss the bus.

Outcomes I will be able to: 1) Use properties of measurement to justify segment length 2) Use properties of measurement to justify angle relationships 3) Justify statements about congruent segments 4) Write the steps of a proof

Properties of Length In the diagram below AC = BD. Use Segment Addition to prove AB = CD Given Reflexive Property Subtraction Property Segment Addition Postulate Substitution Property Simplify AC = BD BC = BC AC - BC = BD - BC AB + BC = AC; BC + CD = BD AB + BC – BC = BC +CD – BC AB = CD

Properties of Angle Measure Reflexive Property Symmetric Property Transitive Property For any angle A, m ∠ A = m ∠ A. If m ∠ A = m ∠ B, then m ∠ B = m ∠ A. If m ∠ A = m ∠ B and m ∠ B = m ∠ C, then m ∠ A = m ∠ C.

Example Angle Addition Postulate Substitution m ∠ ABC = m ∠ DBE m ∠ ABC + m ∠ CBD = m ∠ DBE + m ∠ CBD m ∠ CBE = m ∠ DBE + m ∠ CBD m ∠ ABD = m ∠ CBE

Properties of Angle Measures Real-Life Example AUTO RACING: The Talladega Superspeedway racetrack in Alabama has four banked turns, which are described in the diagram below. Use the given information about the maximum banking angle of the four turns to find m<4. Given information: How can we find angle 4?

Proofs Theorem – A true statement that follows as a result of other true statements. Two-Column Proof – Two columns of statements and reasons that show the logical order of an argument. Paragraph Proof – Writing statements and reasons in complete sentences, showing the logical order of an argument.

Properties of Segment Congruence Reflexive Property Symmetric Property Transitive Property

Prove the Symmetric Property of Segment Congruence Given: Prove: Statements PQ = XY 3. XY = PQ 4. Reasons 1. Given 2.Definition of Congruence 3. Symmetric Prop of Equality 4. Definition of Congruence

Proofs: In the figure below, prove if we are given EF = GH Statements 1. EF = GH 2. EF + FG = GH + FG 3. EG = EF + FG, FH = GH + FG 4. EG = FH 5. Reasons 1. Given 2. Addition Prop. 3. Segment Addition Postulate 4. Substitution Prop. 5. Definition of Congruent Segments

Proofs Given : Statements: RT = WY 3. RT = RS + ST; WY = WX + XY 4. RS + ST = WX + XY 5. ST = WX 6. RS = XY 7. Prove: Reasons: 1. Given 2. Def of Congruence 3. Segment Addition Postulate 4. Substitution 5. Given 6. Subtraction Prop from 4 7. Def of congruent Segments

Extra Practice LK = 5 JK = 5 Definition of Congruence J L K

Extra Practice If it helps, draw a picture: Given Definition of midpoint Segment addition Substitution Simplify(combine like terms) Division Property of Equality Substitution

Proof Practice With a partner, complete the proofs practice When finished, make sure to check your answers against my answer key You will be putting one on the board and explaining it to the class