Wedge Dash Diagram of 1,2-Dichloroethane
The teacher's drawing is correct.  Of course there are other possible conformers that could be drawn, but there is nothing wrong with the one that is pictured.   Basic rule:  a dashed wedge indicates a bond projecting behind the plane of the screen, a bold wedge indicates a bond projecting out in front of the plane of the screen, and a simple solid line indicates a bond existing in the plane of the screen.  Also note that this drawing notation can be used for any molecule, not just carbon systems.