There is a technique used often during the renaissance that allowed artists to transfer their 'cartoons' (a full-size and often completed drawing of the composition) to walls or canvas (see here, for example).
This technique is known as pouncing, and involves perforating the lines of the cartoon (in your example the triangle), fastening it to the surface of the support (i.c. the black illustration board), and wiping charcoal powder along the surface so it penetrates the holes.
The resulting dots of charcoal powder on the support can then be connected by pencil or brush.
In your case, you only need to replace the charcoal powder by chalk powder.
Detail of drawing by Raphael. Source.
Alternatively, what you can try is covering the back of your design with chalk powder, laying it on top of the black illustration board, and using a somewhat blunt pencil or tortillon to trace the lines of your design. Depending on the surface of the illustration board (that I'm not familiar with) you might be able to get a somewhat legible tracing.