A version of the Two-Transversal Proportionality Corollary states, "If three or more parallel lines intersect two transversals, then they divide the _______ proportionally."
transversals
Transversals
A version of the Two-Transversal Proportionality Corollary states, "If three or more parallel lines intersect two transversals, then they divide the transversals proportionally."
To answer this question, let's first understand the concept of parallel lines and transversals. Parallel lines are two lines in a plane that never intersect, meaning they maintain the same distance apart at all points. A transversal is a line that intersects two or more parallel lines.
The Two-Transversal Proportionality Corollary is a theorem that deals with the ratios formed when parallel lines are intersected by two transversals. According to the corollary, if three or more parallel lines are intersected by two transversals, then they divide the transversals proportionally.
To understand what is being divided proportionally, we need to examine the line segments formed by the parallel lines and the transversals. By intersecting the parallel lines with the transversals, various line segments are created between these lines. The corollary states that these line segments are divided proportionally.
In other words, if we label the line segments formed by the intersections of the parallel lines and the transversals, let's say AB, BC, CD, DE, and EF, then the corollary tells us that:
AB/BC = CD/DE = EF/FG
Each ratio formed by these line segments is equal, indicating that the parallel lines divide the transversals proportionally.
To answer the question directly, the blank in the corollary can be filled with "transversals" or "lines" since they are the segments being divided proportionally.