I can create a triangle with the Shape Tool in Marquee -- but, I would like the three corners to be rounded (not pointed).

Anyone know how to do this?

In marquee use the pen tool to draw your triangle. Use the selection tool to select the entire triangle object. Under the object tab I believe, I'm not in front of Avid right at the moment, is the option to add radius to corners. Select the amount of curve you would like and there you go.

The Rounded Corners Function only works with Squares and Rectangles -- it will not work on Triangles.

Bump

My reply is what happens when you make assumptions. Indeed the corner radius only works with squares or rectangles. You could create a round cornerd triangle by drawing a circle the size of your corner radius. Duplicate it 2 more times and place them at  the positions you want your corners to be. Use the pen tool to draw lines that connect the circles to each other to create your triangle with rounded corners. Select all and group when finished so they all move together when you want to scale or move. Beware, this does some odd things if you add extrusions to the grouped shape.

Have not tried it in Marque but in Illustrator (believe Marquee works the same)

I would draw a triangle as a guide. 

Then with the pen tool draw another triangle over the original with points just short of each apex and use the bezier function at each point to create your rounded corners.

Delete the original triangle