artist,
View>Smart Guides are your friends.
You may, with the triangle you wish to move and rotate:
1) Without selecting the triangle in any other way first, ClickDrag the first corner Anchor Point you wish to position with the normal Selection Tool to where you want it (Smart Guides say anchor for an Anchor Point and path for a path segment when you are there);
2) Switch to the Rotate Tool and click the Anchor Point from 1) to make it the centre of rotation, then ClickDrag the triangle the other corner Anchor Point you wish to position until you reach the desired spot;
3) If you wish to have the two triangles at a distance while keeping the angle, just switch back to the Selection Tool and drag it a bit, or use Object>Transform>Move or something else.