Question

1. Provide reasons for the proof. Given:

Answer 1

Answer:

1.   given

2.  corresponding angles

3.  definition of congruent angles

4.  adjacent angles on a straight line

5.  definition of linear pair

6.  definition of supplementary angles

7.  substitution property

8.   definition of supplementary angles

Step-by-step explanation:

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Answer 2

Given that Line m is parallel to line n.
We  prove that 1 is supplementary to 3 as follows:

$\begin{tabular} {|c|c|} Statement&Reason\\[1ex] Line m is parallel to line n&Given\\ \angle1\cong\angle2&Corresponding angles\\ m\angle1=m\angle2&Deifinition of Congruent angles\\ \angle2\ and\ \angle3\ form\ a\ linear\ pair&Adjacent angles on a straight line\\ \angle2\ is\ supplementary\ to\ \angle3&Deifinition of linear pair\\ m\angle2+m\angle3=180^o&Deifinition of supplementary \angle s\\ m\angle1+m\angle3=180^o&Substitution Property \end{tabular}$
$\begin{tabular} {|c|c|} \angle1\ is\ supplementary\ to\ \angle3&Deifinition of supplementary \angle s \end{tabular}$