Given the following diagram (note that the intersection point of the segment that connects triangles XYB and ABC on the segment AB should be point I), where the triangles are all equilateral, and the points H, I, and J bisect the segments AC, AB, and XB, respectively:

http://img651.imageshack.us/img651/9529/triangle.jpg
Identity the following translations and rotations:

* $\displaystyle R_{A, \frac{\pi}{2}} \circ R_{B, \frac{\pi}{2}}$

* $\displaystyle R_{C, \frac{\pi}{2}} \circ R_{A, \frac{\pi}{2}}$

* $\displaystyle R_{A, \frac{\pi}{2}} \circ T_{CA}$

* $\displaystyle R_{A, \frac{\pi}{3}} \circ R_{B, \frac{\pi}{3}}$

* $\displaystyle R_{A, \frac{\pi}{2}} \circ R_{B, \frac{\pi}{6}}$

* $\displaystyle R_{A, \frac{3\pi}{4}} \circ R_{B, \frac{\pi}{4}}$

I am absolutely confused and lost in the modern geometry class and have no idea how to approach these.

Edit: Is $\displaystyle R_{A, \frac{\pi}{2}} \circ R_{B, \frac{\pi}{2}} = R_{J, \frac{4\pi}{3}}$ ?