David, I tried to re-create your steps, and here's what I found to work.

1.) Draw your default triangle.

2.) Create your shape data entries. For simplicity, I made the "names" X1, Y1, X2 ... etc. Six entries. I added 3 more entries, the lengths of each side. For convenience, make the values that you enter identical to your drawn shape. Also, you might want to check the box: ask on drop.

3.) Open the shape sheet:

Shape Transform:

Use the max fcn for both width and height. Width will be the greater of X2-X1 and X3-X1. Likewise for height. You may want to guard these fcns. Don't forget the Prop prefix.

Geometry1 Section

Set the 1st X & Y entries to Prop.X1 and Prop.Y1. Likewise for the next two vertices. The last will remain unchanged as it closes the shape back to the 1st point. You may want to guard these entries too. I didn't try this though.

Shape Data Section

Enter formulas for the three line length rows in the value cells. For exmaple: L1= SQRT((Prop.X2-Prop.X1)^2+(Prop.Y2-Prop.Y1)^2)

Your triangle should maintain it's shape for any angular rotation. When you bring the Shape Data table back up, the lengths will be updated. This ought to meet your basic requirements.