Answer:
The two column proof can be presented as follows;
Statement [tex]{}[/tex] Reason
1. p║q [tex]{}[/tex] Given
∠1 ≅ ∠11
2. ∠1 ≅ ∠9 [tex]{}[/tex] Corresponding angles on parallel lines
3. ∠9 ≅ ∠11 [tex]{}[/tex] Transitive property of equality
4. a║b [tex]{}[/tex] Corresponding angles on parallel lines are congruent
Step-by-step explanation:
The statements in the two column proof can be explained as follows;
Statement [tex]{}[/tex] Explanation
1. p║q [tex]{}[/tex] Given
∠1 ≅ ∠11
2. ∠1 ≅ ∠9 [tex]{}[/tex] Corresponding angles on parallel lines crossed by a common transversal are congruent
3. ∠9 ≅ ∠11 [tex]{}[/tex] Transitive property of equality
Given that ∠1 ≅ ∠11 and we have that ∠1 ≅ ∠9, then we can transit the terms between the two expressions to get, ∠9 ≅ ∠11 which is the same as ∠11 ≅ ∠9
4. a║b [tex]{}[/tex] Corresponding angles on parallel lines are congruent
Whereby we now have ∠9 which is formed by line a and the transversal line q, is congruent to ∠11 which is formed by line b and the common transversal line q, and both ∠9 and ∠11 occupy corresponding locations on lines a and b respectively which are crossed by the transversal, line q, then lines a and b are parallel to each other or a║b.
