stem construct a triangle given side a, altitude to side b, and the median to side c
Well, constructing a triangle given all those specific conditions sounds like a real puzzle! It reminds me of trying to solve a Rubik's Cube while riding a unicycle. But here's how I would tackle it:
Step 1: Draw side a as the base of your triangle. Let's call it AB.
Step 2: From point B, draw a perpendicular line upwards (because it's an altitude) and label the intersection point with side a as point D.
Step 3: Using point D, construct a line parallel to side a. This new line will intersect side b at some point, let's call it E.
Step 4: Now, draw a line segment connecting point E with the midpoint of side a, let's say F. This line segment will represent the median to side c.
Step 5: Finally, connect points A and F to complete your triangle, and voila! You've successfully constructed a triangle with the given conditions.
Now, constructing this triangle might not be as easy as constructing a tower of Jenga blocks, but I'm sure you'll tackle it with the grace of a professional circus performer! Good luck!