Proportions with an Angle Bisector in a Triangle

Use the Geogebra page below to discover a proportion relationship of angle bisectors in triangles.
Drag the vertices of the triangle and observe point D. 1). Is point D always the midpoint of segment BC? 2). Drag some more. Under what conditions will point D be the midpoint of segment BC? 3). Move the triangle so that AB is greater than AC. How does BD compare to CD? 4). Your answer to question 3 may give you an idea for a proportion. Use the input bar to measure the ratios involving AB, AC, BD, and CD to see if you can create equal ratios (a proportion). 5). Try writing your idea as a conjecture.