Question

problem 1
problem 2
which problem could be solved by using the side splitter theorem? why?
problem #1 because mn || bc so the sides are divided proportionally.
problem #2 because mn || bc so the sides are divided proportionally.
problem #1 because the sides seem to be divided proportionally.
problem #2 because the sides seem to be divided proportionally.

Explanation:

Step1: Recall the Side - Splitter Theorem

The Side - Splitter Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

Step2: Analyze Problem #1

In Problem #1, there is no indication that \(MN\parallel BC\). Just because the sides "seem" to be divided proportionally is not a valid geometric reason. The Side - Splitter Theorem requires a parallel line.

Step3: Analyze Problem #2

In Problem #2, the arrows on \(MN\) and \(BC\) indicate that \(MN\parallel BC\). By the Side - Splitter Theorem, the line \(MN\) (which is parallel to \(BC\)) divides the sides \(AB\) and \(AC\) proportionally.

Answer:

Problem #2 because \(MN\parallel BC\) so the sides are divided proportionally.