The triangles are just indicators, like a road sign that says, "Dead End". They let the editor know there aren't any more frames of video beyond the in point or the out point or both (whichever ones have the triangle).
An easy way to create the handles necessary for a transition is just to overlap the outgoing clip with the incoming clip by however many frames are needed for the transition. So if you need a 30-frame transition, set the playhead 30 frames prior to the out point of the outgoing clip and then drag/drop the incoming clip on top of the outgoing clip by lining up the in point of the incoming clip with the playhead.
Drop the transition at the cut between the clips and set the transition to "Start at Cut".
Jeff