Which statement is true?
A. Interior angles should all be congruent, so neither of these pictures show parallel lines.
B. Same-side interior angles are supplementary so picture i shows parallel lines.
C. Same-side interior angles are supplementary so picture ii shows parallel lines.
D. It doesn't look like any lines will intersect, so both pictures i and ii are parallel lines.
The correct answer is option C. Same-side interior angles are supplementary so picture ii shows parallel lines.
To determine which statement is true, we need to analyze the given options and understand the concepts involved.
Option A states that neither of the pictures show parallel lines because the interior angles are not congruent. To evaluate this statement, we must remember that for lines to be parallel, the corresponding interior angles should be congruent.
Option B suggests that picture i shows parallel lines because the same-side interior angles are supplementary. This statement is partially correct. Same-side interior angles are indeed supplementary, meaning that their sum is equal to 180 degrees. However, the information provided does not allow us to conclude that the lines in picture i are necessarily parallel.
Option C claims that picture ii shows parallel lines because same-side interior angles are supplementary. Similarly to option B, the statement is partially correct. Same-side interior angles are indeed supplementary, but it doesn't necessarily imply that the lines are parallel.
Option D suggests that both pictures i and ii show parallel lines because it seems like no lines will intersect. This statement is incorrect. The absence of apparent intersections does not guarantee that the lines are parallel.
Based on our analysis, none of the options provide a completely accurate answer. However, we can draw a conclusion based on the information given. Since none of the interior angles in either picture are congruent, we can infer that option A is the closest to being true. Therefore, the correct answer is:
A. Interior angles should all be congruent, so neither of these pictures show parallel lines.
The correct answer is:
C. Same-side interior angles are supplementary so picture ii shows parallel lines.