If you are given: 12 = 3(x 9)
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1 Name [PACKET 2.2: INTRO TO PROOFS] 1 A, is a convincing argument that uses deductive reasoning. Every statement you make must be justified with a valid property. The following properties will be super valuable: Property Example If you are given: x 5 = 12 If you are given: x + 6 = 15 If you are given: ⅕x = -2 If you are given: 2x = 8 If you are given: y = 2x + 2 and x = 5 Other Important Properties If you are given: 30 If you are given: 5 = x If you are given: y = j and j = -13 If you are given: 12 = 3(x 9) If you are given: y = 3(4) - 12 If you are given: 100 = 45x 20x The Algemazing-Postulate * Always conclude: Coolness '()*+,-. > Coolness (1-,(2) * The last postulate has yet to be proven, but the teachers of this course are pretty sure it s true based on how highly we think of ourselves. We are currently refusing outside input regarding this postulate.
2 2 PACKET 2.2: INTRO TO PROOFS Tell which property justifies each conclusion. Given: 6x + 2 = Given: 45 = x Conclusion: 6x = 10 Conclusion: x = Given: 3x 7x = Given: 4(q - x) = r Conclusion: -4x = 20 Conclusion: 4q - 4x = r 5. If a = r and r = 60, 6. If B is the midpoint of GH, then a = 60. then 2 Column Proofs (???) A two-column proof lists each statement on the left with a justification on the right. Each step follows logically from the line before it. Fill in the missing statements or reasons for the following two-column proof. Given: (x -10) = 85 Prove: x = 30 ß This line tells you everything that has been, or everything that is known to be true. ß This line tells you what you must. Example # (x -10) = (x -10) = x - 20 = x = x = Given: 4x 2(2 x) = 4x -24 Prove: x = -10 Example # (2 x) = x = x =
3 [PACKET 2.2: INTRO TO PROOFS] 3 Given: 3x + 4y = 23; x = 1 Prove: y = 5 Example #3 2. 3(1) + 4y = y = y = Now, summarize your notes here! Solve each equation for x! Multiply! Factor! 10x 3 = x + -4 = 3x x(x 3) 4. 2x 2 32x 5. Graph the equation: y = -x 6. Graph the equation: y = -2
4 4 PACKET 2.2: INTRO TO PROOFS Practice 2.2: Introduction To Proofs Support each conclusion with a valid reason. Given: x - 42 = Given: 23(2 + x) = Given: 3x 7x = 20 Conclusion: x = 54 Conclusion: 2 + x = 10 Conclusion: -4x = Given: -x = If 12 = d and d = x, 6. GH GH Conclusion: x = -34 then 12 = x. Fill in the missing statements or reasons for the following two-column proof. Proof #1 Given: 4x -20 = 100 Prove: x = 30 4x 20 = x = x = Proof #2 Given: 12 - x = 10 Prove: x = x = x = 2 3. Given: 5x + 20 = x Prove: x = 0 Given: 12 - x = 10 Prove: x = 2 Proof #3 2. 3x = -2x x= Proof # = 10 + x = x Given: 10 3(4x 2) + 1 = 77 Prove: x = (4x 2) + 1 = (4x 2) = x + 6 = x =
![[PACKET 2.2: INTRO TO PROOFS] 5 Application 2.](/docs-images/96/127304494/images/5-1.jpg "2: Introduction To Proofs Support each conclusion")
5 [PACKET 2.2: INTRO TO PROOFS] 5 Application 2.2: Introduction To Proofs Support each conclusion with a valid reason. Given: 34x = Given: x = Given: 3(x 2) = 21 Conclusion: x = 2 Conclusion: 3.14 = x Conclusion: 3x - 6 = 21 Geometry Properties. Draw a picture to represent each situation and then tell WHY each conclusion can be made: 4. Given: AB is the bisector of DAC 5. H is the midpoint of QR 6. Given: Point B is on AC Conclusion: DAB CAB Conclusion: QH HR Conclusion: AB + BC = AC : : : Write the reasons for the proofs below: A B Given: Prove: m 1 = m 3 m AEC = m DEB 1 C 2 3 E D m 1 = m 3 m 2 = m 2 m 1 + m 2 = m 3 + m m 1 + m 2 = m AEC m 3 + m 2 = m DEB m AEC = m DEB 5. 6.
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