2761.11 – A Sum of Slopes

Suppose the base of an equilateral triangle is on the $x$ -axis. What is the sum of the slopes of all three sides of the triangle?

Solution

Set up the triangle as in the figure below. We know $m_1 = 0$ . Note that $m_2 = b/a$ , and $m_3 = -b/a$ . We don't need to know what $a$ and $b$ are. Clearly, $m_1 + m_2 + m_3 = 0$ .