The shape is a triangle with a line in the middle. How do I write an indirect proof with this information?
triangle LMN . MP is down the middle
Given:
NP > LP
Prove:
MP is not a median
To write an indirect proof, we start by assuming the opposite of what we want to prove and then show that it leads to a contradiction or inconsistency. In this case, we want to prove that MP is not a median. Let's assume the opposite, which is that MP is a median of triangle LMN.
Now, let's examine the properties of medians in a triangle. A median in a triangle is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. Since we assumed that MP is a median, it would connect vertex M to the midpoint of side LN.
Based on the information given, NP > LP. This means that the length of side NP is greater than the length of side LP. However, since MP is a median, it cuts LN into two equal halves, meaning that the length of NP should be equal to LP. This creates a contradiction since we have assumed that NP > LP.
This contradiction arises from assuming that MP is a median, and it leads us to conclude that our assumption is incorrect. Therefore, MP cannot be a median of triangle LMN. Thus, we have proven our statement.