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Chapter 2 Review

Chapter 2 Review. Reasoning and Proof. Vocab: State whether each sentence is true or false. If false, replace the incorrect word to make it true. Theorems are accepted as true. In a two-column proof, the properties that justify each step are called reasons.

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Chapter 2 Review

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  1. Chapter 2 Review Reasoning and Proof

  2. Vocab:State whether each sentence is true or false. If false, replace the incorrect word to make it true. • Theorems are accepted as true. • In a two-column proof, the properties that justify each step are called reasons. • The Reflexive Property of Equality states that for any number a, a=a. • The contrapositive of a conditional is formed by switching the hypothesis and conclusion of the original statement.

  3. Inductive Reasoning and Conjecture: Make a conjecture based on the given information. Draw a figure if necessary. • and are supplementary • X, Y and Z are collinear and XY = YZ

  4. Conditional Statements: a)Write each statement in if-then form, then identify the hypothesis and conclusion. b)Write the converse of the statement. If it is false give a counterexample. • March has 31 days. • The intersection of two planes is a line.

  5. Postulates:Determine if each statement is always, sometimes, or never true. Explain.(use a postulate or theorem to explain when possible) • The intersection of two different lines is a line. • If P is the midpoint of XY, then XP=PY. • Four points determine exactly one plane. • If MX = MY, then M is the midpoint of XY.

  6. Algebraic Properties and Proof: State the property that justifies each statement. • If 3(x +2)=6, then 3x+6= 6 • If 10x = 20, then x = 2 • If AB + 20 = 45, then AB = 25 • If 3 = CD, and CD=XY, then 3 = XY

  7. Algebraic Proof: Write a two-column proof. • If AC = AB, AC = 4x+1 and AB = 6x-13, then x = 7.

  8. Proving Segment Relationship: Write a two-column proof • Given: AB=CD Prove: AC = BD A B C D

  9. Angle Relationship: Find the measure of the numbered angle • Angle 1 • Angle 2 • Angle 3 A D F 2 3 73 1 C B E

  10. Proving Angle Relationships: Write a two-column proof F • Given: Prove: E C A B

  11. ANSWERS • Slide 1: • 1. Postulates are accepted as true. • 2. True • 3. True • 4. The converse of a conditional is formed by switching the hypothesis and conclusion of the original statement.

  12. ANSWERS • Slide 2: • 1. Angles A and B are a linear pair. • 2. Y is the midpoint of XZ.

  13. ANSWERS • Slide 3: • 1. a) If it is March, then the month has 31 days. - hyp- It is March concl.- the month has 31 days b) If the month has 31 days, then it is March. -false= There are 31 days in the month of July • a) If two planes intersect, then the intersection is a line. -hyp- two planes intersect concl.- it is a line b) If the intersection is a line, then two planes intersected. -true

  14. ANSWERS • Slide 4: • 1. Never, because the intersection of two lines is exactly one point. • 2. Always, that is the definition of a midpoint. • 3. Sometimes, because 3 points determine exactly one plane, the fourth point could be on a second plane. • 4. Sometimes, X and Y could be collinear so the lines with X and Y would be intersecting at M and therefore M would not be a midpoint.

  15. ANSWERS • Slide 5: • 1. Distributive Property • 2. Division Property • 3. Subtraction Property • 4. Transitive Property

  16. ANSWERS • Given: AC = AB, AC = 4x + 1, AB = 6x – 13 • Prove: x = 7 • AC = AB, AC = 4x + 1, 1. Given AB = 6x – 13 • 4x + 1 = 6x – 13 2. Substitution Prop • 4x + 1 – 4x= 6x – 13 – 4x 3. Subtraction Prop • 1 = 2x – 13 4. Substitution Prop • 1 + 13 = 2x – 13 + 13 5. Addition Prop • 14 = 2x 6. Substitution Prop • 14/2 = 2x/2 7. Division Prop • 7 = x 8. Substitution Prop • x = 7 9. Symmetric Prop

  17. ANSWERS • Slide 7: • AB = CD 1. Given • AB + BC = AC 2. Segment Addition Postulate BC + CD = BD • CD + BC = AC 3. Substitution Prop • AC = BD 4. Substitution Prop Given: AB = CD Prove: AC = BD A B C D

  18. ANSWERS • Slide 8: • 1. angle 1 + 73 = 90 angle 1 = 17 • 2. perpendicular lines =rt angles angle2 = 90 • 3. angles 2 and 3 are vertical angles. Vertical angles are congruent. angle 3= 90

  19. ANSWERS C F E Given: Prove: • ABF is congruent to EBC 1. Given • ABF = EBC 2. Definition of congruent angles 3. ABE + EBF = ABF 3. Angle Addition Postulate EBF + FBC = EBC 4. ABE + EBF = EBF + FBC 4. Substitution Prop 5. ABE + EBF – EBF = 5. Subtraction Prop EBF + FBC - EBF 6. ABE = FBC 6. Substitution Prop A B *Angle symbols should be used in front of each set of 3 letters

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