Final answer:
The statement about same-side interior angles being complementary when two parallel lines are intersected by a transversal is false; they are supplementary. Also, only knowing the angles of two vectors is insufficient to determine the angle of their resultant vector without more information.
Step-by-step explanation:
The statement about two parallel lines intersected by a transversal such that the same-side interior angles are complementary is false. When two parallel lines are intersected by a transversal, the same-side interior angles are supplementary, not complementary. Supplementary angles add up to 180 degrees, whereas complementary angles add up to 90 degrees. In geometry, two lines are parallel if they never intersect, no matter how far they are extended, and a transversal is a line that intersects two or more lines at distinct points. The angles formed by the intersection of the parallel lines and the transversal have special relationships.
In vector mathematics, knowing only the angles of two vectors does not suffice to find the angle of their resultant addition vector without additional information; thus, the statement is false. However, if the vectors are perpendicular, forming a 90-degree angle, we can use the Pythagorean theorem to calculate the length of the resultant vector, which makes the statement true in that specific case. Moreover, a vector can indeed form the shape of a right-angle triangle with its x and y components, and this concept is critical when decomposing vectors into their orthogonal components.