Write a two column proof for: Given t is parallel s; angle 5 is congruent to angle 6. Prove: l is parallel m.

Statements Reasons
1. t is parallel 1. Given
to s
2.

no idea what the angles are.

if they are alternate interior or exterior, then that is enough.

they are alternate interior

angle 5 is congruent 2. Given

to angle 6
3. Angles formed by 3. Definition of parallel lines:
a transversal cutting If a transversal cuts two
two parallel lines have parallel lines, then the
the same measure corresponding angles are
congruent.
4. Angle 5 and angle 6 4. Substitution (using statement 2)
are corresponding angles
created by a transversal cutting parallel lines.
5. Angles 5 and 6 are 5. Definition of congruent angles:
congruent If two angles have the
same measure, then they
are congruent.
6. Corresponding angles 6. Definition of corresponding angles:
are congruent If two angles are congruent
and formed by a transversal
cutting two parallel lines,
then the lines are parallel.
7. l is parallel to m 7. Substitution (using statement 6)