Deductive Reasoning

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

2.2cWritten Ex. Justify each step. The question you need to ask is… What did I do to get to the next step? +5 +5 4x – 5 = - 2 Given 1 4x = 3 Addition Prop. Of Equality ___ __ 4 4 Division Prop. Of Eq. 2 2 2 Given Multiplication Prop. Of Equality 3 3 Division Prop. Of Eq.

Justify each step. The question you need to ask is… What did I do to get to the next step? 3 3 Given 3 Z + 7 = - 33 Multiplication Prop. Of Equality -7 -7 z = - 40 Subtr. Prop. Of Equality 15y + 7 = 12 – 20y Given 4 +20y +20y Addition Prop. Of Equality 35y + 7 = 12 - 7 - 7 Subtr. Prop. Of Equality 35y = 5 ___ ___ 35 35 Division Prop. Of Eq.

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

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

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

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

10 Given: Prove: K g +180 ? 4 5 ? 6 Label diagram to help visualize. L J Statements Reasons Given Angle Add. Postulate Substitution Prop. Of Eq. Reflexive Prop. Of Eq. Subtr. Prop. Of Eq. Notice that the To Prove or Conclusion is ALWAYS the last statement

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

12 Given: Prove: RP = TQ PS = QS ? g ? g RS = TS Label diagram to help visualize. g g Statements Reasons Given RP = TQ Given PS = QS RP + PS = TQ + QS Add. Prop. Of Eq. RP + PS = RS Segment Add. Postulate TQ + QS = TS Segment Add. Postulate RS = TS Substitution. Prop. Of Eq. 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.

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

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

C’est fini. Good day and good luck.

Deductive Reasoning