Inspired by Sam's Attacks and Counterattacks, my lesson on medians and altitudes was much more student centered than before.
To begin class, I showed this image and asked students to work with their partners to write an if-then definition for median.
After, they passed their paper to another pair with a new goal to try to draw diagram that fulfills the definition before them but that clearly isn't a median. Some definitions weren't specific enough (omitted the word triangle or "from the vertex"). While others assumed that all triangles would be equilateral and hence that a median bisects the triangle. I walked around and helped students who needed help thinking of ways to disprove faulty definitions.
Then the papers were returned to their original owners for them to improve their wording. I gathered student responses and together we agreed on a definition to add to our flashcard deck: "If a segment is drawn from the vertex of a triangle and divides the opposite side into two congruent sides, then it is a median."
With the definition for median established, students easily decided on a definition for altitude.
Next class will be drawing medians and altitudes with rulers and protractors...