This is off the top of my head, w/o the Sketchpad up and running. 1. Construct segment AB for base. 2. Construct a segment CD for the desired median (since base angle must be acute, this segment has to be shorter than AB). 3. On CD, dilate C 1/3 distance to D. Since medians intersect in 2:1 ratio. 4. From A, construct a circle with center at A and radius = CC'. Same from B. Where two circles intersect is where medians intersect. 5. Call point of intersection E. Now from A and B dilate E to create segments AE' and BE' that are equal to CD. 6. Draw a ray AE' and BE', label intersection F and AFB is isosceles.
7. You can change the length of CD to create different triangles.