Question

How can finding the slopes of MN and AB help in proving that MN is the midsegment of triangle ABC?

Answer 1

Answer:   The slopes of two parallel lines are equal.

Step-by-step explanation: Let $m_{1}$ and $m_{2}$ be the slopes of lines AB and MN respectively. We know that if the slopes of two parallel lines are equal, then the lines must be parallel. Thus, if we get           $m_{1}=m_{2}$ , then AB is parallel to MN. Also, if we already have M and N as the mid-points of AC and BC, the with the help of slopes of AB and MN, we arrive at our proof that MN is the mid-segment of Triangle ABC. Please see the figure for details.

Answer 2

Mid-segment and bottom side of the triangle is always parallel to each other, and parallel lines must have same slopes, so if their slopes are equal, then MN would be mid-segment of side AB in Triangle ABC

Hope this helps!