advertisement

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 • AC = BD • Given • BC = BC • Reflexive Property • AC - BC = BD - BC • Subtraction Property • AB + BC = AC; BC + CD = BD • Segment Addition Postulate • AB + BC – BC = BC +CD – BC • Substitution Property • AB = CD • Simplify Properties of Angle Measure • Reflexive Property • For any angle A, m∠A = m∠A. • Symmetric Property • If m∠A = m∠B, then m∠B = m∠A. • Transitive Property • If m∠A = m∠B and m∠B = m∠C, then m∠A = m∠C. Example m∠ABC = m∠DBE m∠ABC + m∠CBD = m∠DBE + m∠CBD Angle Addition Postulate m∠CBE = m∠DBE + m∠CBD m∠ABD = m∠CBE Substitution 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 For any segment AB, AB AB • Symmetric Property If AB CD, then CD AB • Transitive Property If AB CD and CD EF , then AB EF Prove the Symmetric Property of Segment Congruence • • • • • • • Given: PQ XY Prove: XY PQ Statements 1. PQ XY 2. PQ = XY 3. XY = PQ 4. XY PQ • • • • • Reasons 1. Given 2.Definition of Congruence 3. Symmetric Prop of Equality 4. Definition of Congruence Proofs: In the figure below, prove EG FH 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. EG FH • • • • Reasons 1. Given 2. Addition Prop. 3. Segment Addition Postulate • 4. Substitution Prop. • 5. Definition of Congruent Segments Proofs Given : RT WY and ST WX Statements: 1. RT WY 2. RT = WY 3. RT = RS + ST; WY = WX + XY 4. RS + ST = WX + XY 5. ST = WX 6. RS = XY 7. RS XY Prove: RS XY 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 K J L LK = 5 JK = 5 Definition of Congruence Extra Practice Given Definition of midpoint Segment addition Substitution Simplify(combine like terms) Division Property of Equality Substitution If it helps, draw a picture: 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