Question

ansversal two lines intersected by are parallel? 2. Error Analysis Noemi wrote, "If 2122. then by the Converse of the Same-side Interior Angles Postulate the error in Noemi's reasoning. 2

Answer 1

The error in Noemi's reasoning is that ∠1 and ∠2 are not congruent by the Converse of the Same-side Interior Angles Postulate. Instead, ∠1 and ∠2 are supplementary angles.

In Mathematics and Euclidean Geometry, the Converse of the Same-side Interior Angles Postulate states that two lines are parallel when two lines and a transversal form supplementary same side interior angles.

By applying the Converse of the Same-side Interior Angles Postulate to the two parallel lines l and m cut through by a transversal, we have the following supplementary angles:

m∠1 + m∠2 = 180°.

In this context, we can logically deduce that Noemi's reasoning is incorrect because ∠1 and ∠2 are not congruent angles based on the Converse of the Same-side Interior Angles Postulate. Instead, ∠1 and ∠2 are supplementary angles.

Answer 2

L is not parallel to m because ∠1 and ∠2 are not supplementary, they are congruent.

Step-by-step explanation:

Taking into account the figure, ∠1 and ∠2 are same-side interior angles. However, the error in Noemi's reasoning is that the converse of the same-side interior angles says that when these angles are supplementary, the lines are parallel.

So, we can't say that l || m because ∠1 and ∠2 are not supplementary, they are congruent.

Where congruent means that they have the same measure and supplementary means that they add to 180 degrees.