There is the perfect tool for it: "Normal Align" in the Tools->Align menu ( or use the alt-N keyboard shortcut )
- for your example select the blue box you want to have aligned and press alt-N / use the menu entry
- now you'll see a blue arrow appear on the blue box ( the source object )
- click on it and drag to position it on the source object's side you want to have aligned
- now click on the target object ( your purple object ) and see a green arrow appear
- click & drag it to the target polygon ( in your case the slanted side ), you want to have the source object aligned to
- Now when you release the mousebutton, the source object will snap to the target object and a dialog will open, providing some more usefull options for the align
Press okay when you are satisfied and your are done ...
Josef WienerroitherSoftware Developer & 3d Artist Hybrid