Question

Prove using the two-column method

given: l is parallel to m
prove: angle 1 and angle 4 are supplementary

Answer 1

Given that line l is parallel to line m, we proved that angle 1 and angle 4 are supplementary by using the properties of parallel lines and the concept of alternate interior angles in a two-column proof format.

Step-by-step explanation:

To prove that angle 1 and angle 4 are supplementary given that line l is parallel to line m, we can use properties of parallel lines and the concept of alternate interior angles. Here is the proof in a two-column format:

1. Statement: Line l is parallel to line m.
   Reason: Given.
2. Statement: Angle 3 is congruent to angle 1.
   Reason: If two parallel lines are cut by a transversal, then each pair of alternate interior angles are congruent.
3. Statement: Angle 3 and angle 4 are supplementary.
   Reason: If two angles form a straight line, then they are supplementary.
4. Statement: Angle 1 and angle 4 are supplementary.
   Reason: If two angles are congruent to two angles that are supplementary, then the first two angles are also supplementary.

Thus, the proof demonstrates that angle 1 and angle 4 are indeed supplementary when l is parallel to m.