How can you transform the figures so that they have the same orientation?
Composition of transformations:
Reflection: In the line y=2
Translation: (x,y) → (x+1,y-2)
Congruence transformation?: Yes
Practice makes perfect
Since the pattern shows a tesselation, we know that all orange and blue triangles have to be congruent. Therefore, any composition of transformation that maps △ ABC onto △ CDB is going to be a congruence transformation.
Composition of transformations
Note that a composition of transformations suggests that we should perform at least two transformations to map △ ABC onto △ CDB. By reflecting △ ABC in a horizontal line, such as y=2, we can make sure it has the same orientation as △ CDB.
When △ A'B'C' and △ CBD have the same orientation, we can map A'B'C' onto △ CDB by translating it so that corresponding vertices map onto each other. For example, A' and C are corresponding vertices so by translating △ ABC one unit to the right and 2 units down, the triangles will map onto each other.
The following congruence transformations map △ ABC onto △ CBD.
Reflection:& In the line y=2
Translation:& (x,y) → (x+1,y-2)
