The statements and reasons why the given statements are true are presented in the following two column proofs;
Question 1
Given: 9·(x + 6) - 41 = 75
[tex]Prove \ x = \dfrac{62}{9}[/tex]
Statement [tex]{}[/tex] Reason
S1. 9·(x + 6) - 41 = 75 [tex]{}[/tex] R1. Given
S2. 9·(x + 6) = 116 [tex]{}[/tex]R2. Addition property
S3. 9·x + 54 = 116 [tex]{}[/tex]R3. Distributive property
S4. 9·x = 62 [tex]{}[/tex]R4. Subtraction property
S5. [tex]x = \dfrac{62}{9}[/tex] [tex]{}[/tex] R5. Division property of equality
Question 2.
Statement [tex]{}[/tex] Reason
S1. m∠A + m∠B = m∠D [tex]{}[/tex] R1. Given
S2. ∠C and ∠D form a Linear Pair [tex]{}[/tex] R2. Definition of linear pair
S3. ∠C and ∠D are supplementary [tex]{}[/tex]R3. Linear pair ∠s are supplementary
S4. ∠C + ∠D = 180° [tex]{}[/tex] R4. Definition of supplementary
S5. m∠C + m∠A + m∠B = 180° [tex]{}[/tex] R5. Substitution property
Question 3.
Statement [tex]{}[/tex] Reason
S1. ∠BDA ≅ ∠A [tex]{}[/tex] R1. Given
S2. ∠BDA ≅ ∠CDE [tex]{}[/tex] R2. Vertical angle theorem
S3. ∠CDE ≅ ∠A [tex]{}[/tex] R3. Transitive property of congruency
S4. m∠CDE = m∠A [tex]{}[/tex] R4. Definition of congruency
S5. (13·x + 20)° = (14·x + 15)° [tex]{}[/tex] R5. Substitution Property of Equality
S6. 14·x° = 13·x + 5° [tex]{}[/tex]R6. Subtraction property
S7. x = 5 [tex]{}[/tex] R7. Subtraction property
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