Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Survey

Document related concepts

no text concepts found

Transcript

2.5 – Reasoning Using Properties of Algebra Name Property of Equality Addition Property If a = b, then a + c = b + c Subtraction Property If a = b, then a – c = b – c Multiplication Property Division Property If a = b, then ac = bc Reflexive Property For any real #, a = a Symmetric Property If a = b, then b = a Transitive Property If a = b and b = c, then a = c Substitution Property If a = b, then a/c = b/c If a = b, then b can be substituted in for a PROOFS! All proofs start and end the same. It is very helpful to have a picture to refer to. We are given information and then are told to prove something. Format of Proofs Given: Prove: Picture Statements Reasons 1. What you are given 1. Given 2. 2. 3. 3. … To Prove … Use the property to complete the statement. 2. Addition Property of Equality: TU + 20 If RS = TU, then RS + 20 = ______________. 3.Multiplication Property of Equality: If m1 = m2, then 3m1 = ____________. 3m2 4.Substitution Property of Equality: = 100 If a = 20, then 5a = 5(20) __________. 5.Reflexive Property of Equality: x If x is a real number, then x = _____. 6.Symmetric Property of Equality: If AB = CD, then CD = __________. AB 7.Transitive Property of Equality: If mE = mF and mF = mG, then ________________. mE = mG Complete the logical argument by writing a reason for each step. Statements 1. 8x – 34 = 6 Reasons 1. given __________________ 2. 8x = 40 2. Addition Prop __________________ 3. x=5 3. Division Prop __________________ Complete the logical argument by writing a reason for each step. Statements Reasons 1. 4x – 7 = 6x + 7 1. given __________________ 2. -2x – 7 = 7 2. __________________ Subtraction Prop 3. -2x = 14 3. Addition Prop __________________ 4. x = -7 4. Division Prop __________________ Complete the logical argument by writing a reason for each step. Statements Reasons 1. 5(x – 3) = 4(x + 2) 1. given ___________________ 2. 5x – 15 = 4x + 8 2. Distributive Prop __________________ 3. 4. x – 15 = 8 x = 23 3. ___________________ Subtraction Prop 4. Addition Prop ___________________ 9. Solve the equation. Write a reason for each step 4x – 7 = 6x + 7 Statements Reasons 1. 4x – 7 = 6x + 7 1. Given – 7 = 2x + 7 2. Subtraction Prop. 2. 3. – 14 = 2x 3. Subtraction Prop. 4. –7 = x 4. Division Prop. 10. Solve the equation for y. Write a reason for each step. 12x – 3y = 30 Statements Reasons 1. 12x – 3y = 30 1. Given 2. –3y = -12x + 30 2. Subtraction Prop. 3. y = 4x – 10 3. Division Prop. Complete the proof by writing a reason for each step. GIVEN: AL = SK PROVE: AS = LK Statements Reasons 1. AL = SK 1. given ___________________ 2. LS = LS 2. Reflexive Prop ___________________ 3. AL + LS = SK + LS 3. Addition Prop __________________ 4. AL + LS = AS Addition Prop 4. Segment __________________ 5. SK + LS = LK Addition Prop 5. Segment ___________________ 6. AS = LK 6. Substitution Prop ___________________ Steps for Proofs: 1. Start with given and mark pictures 2. What do the givens tell us? 3. What else do we know by looking at the picture? 4. End the proof with what we are trying to prove