Question

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Answer 1

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

$Prove \ x = \dfrac{62}{9}$

Statement                   ${}$ Reason

S1. 9·(x + 6) - 41 = 75   ${}$  R1. Given

S2. 9·(x + 6)  =  116        ${}$R2. Addition property

S3. 9·x + 54 = 116         ${}$R3. Distributive property

S4. 9·x = 62                   ${}$R4. Subtraction property

S5. $x = \dfrac{62}{9}$                     ${}$ R5. Division property of equality

Question 2.

Statement                                     ${}$        Reason

S1. m∠A + m∠B = m∠D   ${}$                     R1.  Given

S2. ∠C and ∠D form a Linear Pair   ${}$   R2. Definition of linear pair

S3. ∠C and ∠D are supplementary   ${}$R3. Linear pair ∠s are supplementary

S4. ∠C + ∠D = 180°  ${}$                           R4. Definition of supplementary

S5. m∠C + m∠A + m∠B = 180°   ${}$         R5. Substitution property

Question 3.

Statement                                     ${}$ Reason

S1. ∠BDA ≅ ∠A                             ${}$ R1. Given

S2. ∠BDA ≅ ∠CDE                      ${}$  R2. Vertical angle theorem

S3. ∠CDE ≅ ∠A                      ${}$       R3. Transitive property of congruency

S4. m∠CDE = m∠A                    ${}$   R4. Definition of congruency

S5. (13·x + 20)° = (14·x + 15)°      ${}$   R5. Substitution Property of Equality

S6. 14·x° = 13·x + 5°                       ${}$R6. Subtraction property

S7. x = 5                      ${}$                  R7. Subtraction property

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