Question

Angles 1 and 3 are called interior angles on the same side of the transversal. a. If l∥m, what is true about m(∠1)+m(∠3) ? b. Can you show the converse of the result in part a: that if your conclusion about m(∠1)+m(∠3) is satisfied, then l∥m?

Answer 1

The sum of the measures of interior angles on the same side of a transversal is always 180 degrees. If line l is parallel to line m, then angle 1 and angle 3 will have measures that add up to 180 degrees. In the converse, if the sum of the measures of angles 1 and 3 is 180 degrees, then it can be concluded that line l is parallel to line m.

Step-by-step explanation:

The sum of the measures of interior angles on the same side of a transversal is always 180 degrees. So, if line l is parallel to line m, then angle 1 and angle 3 are interior angles on the same side of the transversal and their measures will add up to 180 degrees. Therefore, m(∠1) + m(∠3) = 180 degrees.

In the converse, if the sum of the measures of angles 1 and 3 is 180 degrees, then it can be concluded that line l is parallel to line m. This is because the sum of the measures of interior angles on the same side of the transversal will only be 180 degrees if the lines are parallel.