Deductive Reasoning “The proof is in the pudding.”“Indubitably.” Je solve le crime. Pompt de pompt pompt." Le pompt de pompt le solve de crime!"

2.2cWritten Ex. Justify each step x – 5 = - 2 4x = 3 The question you need to ask is… What did I do to get to the next step? Given Addition Prop. Of Equality Multiplication Prop. Of Equality Division Prop. Of Eq. +5 ___ __

Justify each step. 3 4 Z + 7 = - 33 z = y + 7 = 12 – 20y 35y + 7 = 12 35y = 5 Given Multiplication Prop. Of Equality Subtr. Prop. Of Equality Addition Prop. Of Equality Subtr. Prop. Of Equality Division Prop. Of Eq. The question you need to ask is… What did I do to get to the next step? y - 7 ___ 35 35

Justify each step. 5 6 Given b = 3 5(x – 2) = 2x + 8 Multiplication Prop. Of Equality Division Prop. Of Eq. Distributive Prop. Addition Prop. Of Equality 5x - 10 = 2x + 8 3x - 10 = 8 3x = 18 x = 6 Given Multiplication Prop. Of Equality Distributive Prop. Subtr. Prop. Of Equality Addition Prop. Of Equality Division Prop. Of Eq. The question you need to ask is… What did I do to get to the next step? 3 3( ) 6b +6b ___ 8 8

Given: Prove: 7 ? Label diagram to help visualize. Statements Reasons Angle Add. Postulate Substitution Prop. Of Eq. Notice that the To Prove or conclusion is ALWAYS the last statement

Given: Prove: 8FL = AT FA = LT LAFT Label diagram to help visualize. ? ? FL = AT Statements Reasons LA = LA FL + LA = AT + LA FL + LA = FA AT + LA = LT FA = LTSubstitution Prop. Of Eq. Given Reflexive Prop. Of Eq. Add. Prop. Of Eq. Segment Add. Postulate gg Notice that the To Prove or conclusion is ALWAYS the last statement

Given: Prove: 9DW = ON DO = WN N O D W Label diagram to help visualize. ? ? Statements Reasons DW = DO + OW ON = ___ + ____ DO + OW = OW + WN OW = OW Substitution Prop. Of Eq. Given Reflexive Prop. Of Eq. Subtr. Prop. Of Eq. Segment Add. Postulate g g DW = ON DO = WN OW WN Notice that the To Prove or conclusion is ALWAYS the last statement

Given: Prove: 10 L J K Label diagram to help visualize. ? ? Statements Reasons Substitution Prop. Of Eq. Given Reflexive Prop. Of Eq. Subtr. Prop. Of Eq. Angle Add. Postulate g Notice that the To Prove or Conclusion is ALWAYS the last statement

Given: Prove: 11 Label diagram to help visualize. ? ? Statements Reasons Add. Prop. Of Eq. Given Substitution. Prop. Of Eq. Angle Add. Postulate Given Angle Add. Postulate Steps 4 and 5 are needed to permit/validate the substitution.

Given: Prove: 12 Label diagram to help visualize. Statements Reasons Add. Prop. Of Eq. Given Substitution. Prop. Of Eq. Segment Add. Postulate Given Segment Add. Postulate RP = TQ PS = QS RS = TS RP = TQ PS = QS RS = TS RP + PS = TQ + QS RP + PS = RS TQ + QS = TS Steps 4 and 5 are needed to permit/validate the substitution. Note that this proof was the same as the previous poof except for using segments instead of angles. g g g g ??

Given: Prove: 13 Label diagram to help visualize. Statements Reasons Subtr. Prop. Of Eq. Given Substitution. Prop. Of Eq. Segment Add. Postulate Given RQ = TP ZQ = ZP RZ = TZ ZQ = ZP RQ = TP TP = TZ + ZP RQ = RZ + ZQ RZ + ZQ = TZ + ZP RZ = TZ Segment Add. Postulate Notice this is an application of “the sum of the parts equals the whole.” It is also just like the previous proof. Visually, it is easy to see that if you subtract the smaller segment from the larger segment the result will be obtained ? ?

Given: Prove: 14 Label diagram to help visualize. ?? Statements Reasons Subtr. Prop. Of Eq. Given Substitution. Prop. Of Eq. Angle Add. Postulate Given Angle Add. Postulate

C’est fini. Good day and good luck.