SOLUTION: (indirect proof) given line t cuts the lines a and b &#8736;1 &#8773; <2 Prove: a&#8741;b How can you answer this in the three step process?

You did not tell us which angles are ∠1 and ∠2.  So I'll guess
they are alternate interior angles.  But whatever they are, the
gist of the problem is similar.



Assume for contradiction that a and b are not parallel.
Then if we extend them far enough, they will meet at some 
point P.



m∠1 = m∠2  because measure of congruent angles are equal.

m∠2 + m∠3 = 180° because they form a linear pair

m∠1 + m∠3 = 180°  substituting equals for equals

m∠P + (m∠1 + m∠3) = 180°  the measures of the three angles of a triangle
                         have sum 180°

m∠P + 180° = 180°  substituting 180° for (m∠1 + m∠3), equals for equals.

m∠P = 0°  subtracting equals from equals (180°=180°)

A triangle cannot have an angle with 0 measure.

Therefore we have reached a contradiction to the assumption that a and b
are not parallel.

Therefore the assumption is incorrect and therefore a∥b

Edwin