Write a two-column proof

I just need the answer for question 7

The statements and reasons used in the two column method to prove the given statements are as follows;

6. ∠1 is equal to ∠3 by the substitution property and therefore;

∠1 ≅ ∠2 by the definition of congruent angles

7. ∠2 = ∠4 by subtraction and substitution properties of equality, therefore; ∠2 ≅ ∠4 by the definition of congruency

8. ∠5 = ∠8 by substitution, therefore ∠5 ≅ ∠8 by definition

The two column method makes use of two columns in which logical arguments and reasons are provided to support the statements that is required to be proven.

6. The two column method used to prove the statements are as follows;

Statement [tex]{}[/tex]                                   Reason

∠2 ≅ ∠4    [tex]{}[/tex]                                   Given

∠2 = ∠4    [tex]{}[/tex]                                    Definition of congruency

∠1 ≅ ∠3    [tex]{}[/tex]                                    Given

∠1 = ∠3    [tex]{}[/tex]                                     Definition of congruency

∠1 + ∠2 = 90°    [tex]{}[/tex]                            Angle addition property

∠3 + ∠4 = 90°     [tex]{}[/tex]                         Angle addition property

∠1 + ∠2 = ∠3 + ∠4   [tex]{}[/tex]                     Substitution property of equality

∠1 + ∠2 = ∠3 + ∠2   [tex]{}[/tex]                     Substitution property of equality

∠1  = ∠3   [tex]{}[/tex]                                      Subtraction property of equality

∠1 ≅ ∠3   [tex]{}[/tex]                                      By definition of congruency

7. Statements [tex]{}[/tex]                                            Reasons

∠1 ≅ ∠3  [tex]{}[/tex]                                            Given

∠1 = ∠3  [tex]{}[/tex]                                            Definition of congruency

∠1 and ∠3 are corresponding ∠s[tex]{}[/tex]    Definition of corresponding angles

∠3 and ∠4 are linear pair ∠s [tex]{}[/tex]          Definition of linear pair angles

∠1 and ∠2 are linear pair ∠s [tex]{}[/tex]           Definition of linear pair angles

∠3 + ∠4 = 180° [tex]{}[/tex]                                  Linear pair angles are supplementary

∠1 + ∠2 = 180° [tex]{}[/tex]                                   Linear pair angles are supplementary

∠1 + ∠2 = ∠3 + ∠4 [tex]{}[/tex]                              Substitution property

∠3 + ∠2 = ∠3 + ∠4 [tex]{}[/tex]                              Substitution property

∠2 = ∠4 [tex]{}[/tex]                                                Subtraction property of equality

∠2 ≅ ∠4          [tex]{}[/tex]                                      Definition of congruency

Statement       [tex]{}[/tex]                                      Reason

∠5 ≅ ∠7        [tex]{}[/tex]                                        Given

∠5 = ∠7        [tex]{}[/tex]                                         Definition of congruency

∠5 ≅ ∠8        [tex]{}[/tex]                                        Given

∠5 = ∠8        [tex]{}[/tex]                                         Definition of congruency

∠7 ≅ ∠8         [tex]{}[/tex]                                        Vertical angles theorem

∠7 = ∠8         [tex]{}[/tex]                                         Definition of congruency

∠5 = ∠8         [tex]{}[/tex]                                         Substitution property of equality

∠5 ≅ ∠8 [tex]{}[/tex]                                                Definition of congruency

Learn more about the two column method of proving mathematical statements here:

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You do this you are a pro