Question

In the figure, lines l, m, and n are parallel. A classmate says you can use the corollary to the side-splitter theorem to find x. explain your classmate's error

Answer 1

The issue with using the side-splitter to solve for x is that the side-splitter theorem is used to find lengths of the sides being split by parallel lines. In this case, the x is on a line that is parallel and thus could not be solved for using this theorem. 

If we created a triangle where the tops of the non-parallel lines connected, we would be able to compare the following and solve:

$\frac{M1}{M2} = \frac{N1}{N2}$

However, none of this would help us solve for x using this theorem.