Congruence of Triangles
There are several theorems for triangles congruence. The SSS theorem, for example, guarantees congruence if all the side lengths are equal.
But for this project, we don't have any tool to measure lengths, just angles. So we need to move to another congruence theorem where angles are implied. That's where our protractor would be handy.
There are two logic choices to select from; ASA (Angle Side Angle) or AAS (Angle Angle Side).
I would use any of these because they only need one side length to be common in length.
Recall the ASA theorem states that two triangles that have two congruent angles and the side between them congruent too are congruent.
Similarly, two triangles are congruent (AAS theorem) if two of its angles are congruent and one of the non-included sides are also congruent.
The procedure would be like follows:
* Take the long pieces of wood and cut two pieces of the exact length. We don't need a ruler for that.
* Using the protractor, measure two angles in the reference triangle and place two additional pieces of wood that form the exact angles. If the angles are adjacent to the original piece of wood, you would be using the ASA theorem. If the angles are not adjacent to the original piece (just one of them), then you would be using the AAS theorem.