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This activity takes students through each step of sketching and writing the equation of the following within a triangle: Median, Perpendicular Bisector, and Altitudes.
The following concepts are covered: finding the midpoint of a line segment, writing equations of lines (particularly in point-slope and slope-intercept forms), and recognizing that perpendicular lines will have slopes that are opposite reciprocals.
Students are first to plot the given points and connect them creating a triangle. The directions guide them to either finding the midpoint or relevant slopes.
I had students start independently, then allowed for collaboration, and then we synthesized our findings as a class. My students needed lots of practice of these types of questions, so I had them summarize "five key steps" to finding the equation of an altitude when we were done.
This could also be done as guided notes for direct instruction.