1) c â•‘ d by consecutive interior angles theorem
2) m∠3 + m∠6 = 180° by transitive property
3) ∠2 ≅ ∠5 by definition of congruency
4) t ║ v                            Corresponding angle theorem
5) ∠14 and ∠11  are supplementary      Definition of supplementary angles
6) ∠8 and ∠9  are supplementary       Consecutive  interior angles theorem
Step-by-step explanation:
1) Statement                                   Reason
m∠4 + m∠7 = 180°                   Given
m∠4 ≅ m∠6                        Vertically opposite angles
m∠4 = m∠6                        Definition of congruency
m∠6 + m∠7 = 180°                   Transitive property
m∠6 and m∠7 are supplementary      Definition of supplementary angles
∴ c ║ d                            Consecutive interior angles theorem
2) Statement                                   Reason
m∠3 = m∠8                       Given
m∠8 + m∠6 = 180°                 Sum of angles on a straight line
∴ m∠3 + m∠6 = 180°                Transitive property
3) Statement                                   Reason
p ║ q                           Given
∠1 ≅ ∠5                         Given
∠1 = ∠5                          Definition of congruency
∠2 ≅ ∠1                         Alternate interior angles theorem
∠2 = ∠1                          Definition of congruency
∠2 = ∠5                         Transitive property
∠2 ≅ ∠5                         Definition of congruency.
4) Statement                                   Reason
∠1 ≅ ∠5                          Given
∠3 ≅ ∠4                         Given
∠1 = ∠5                          Definition of congruency
∠3 = ∠4                         Definition of congruency
∠5 ≅ ∠4                         Vertically opposite angles
∠5 = ∠4                         Definition of congruency
∠5 = ∠3                         Transitive property
∠1 = ∠3                          Transitive property
∠1 ≅ ∠3                          Definition of congruency.
t ║ v                            Corresponding angle theorem
5) Statement                                   Reason
∠5 ≅ ∠16                         Given
∠2 ≅ ∠4                         Given
∠5 = ∠16                         Definition of congruency
∠2 = ∠4                          Definition of congruency
EF â•‘ GH Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Corresponding angle theorem
∠14 ≅ ∠16                        Corresponding angles
∠14 = ∠16                         Definition of congruency
∠5 = ∠14                         Transitive property
∠5 + ∠11 = 180°                    Sum of angles on straight line
∠14 + ∠11 = 180°                    Transitive property
∠14 and ∠11  are supplementary      Definition of supplementary angles Â
6) Statement                                   Reason
l ║ m                            Given
∠4 ≅ ∠7                         Given
∠4 = ∠7                          Definition of congruency
∠2 ≅ ∠7                         Alternate angles
∠2 = ∠7                          Definition of congruency
∠2 = ∠4                         Transitive property
∠2 ≅ ∠4                         Definition of congruency
∠2 and ∠4 are corresponding angles   Definition
DA â•‘ EB Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Corresponding angle theorem
∠8 and ∠9  are consecutive  interior angles   Definition
∠8 and ∠9  are supplementary       Consecutive  interior angles theorem.
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