History of Math Riddle Help [Extra Credit]

Hello, I am taking a history of math course and my teacher assigned this over spring break. I figured out the riddle, but I need a postulate or proof showing my work makes sense and it does work out. As you can see from my images, the treasure will lie in the same place regardless of where the hut is (that's saying the red and white rock are next to each other). So, no matter where the hut is, as long as the rocks are in the same location, the treasure will fall in the same spot. I kind of tried to explain what I did so I would remember over break. I really need help figuring the proof out because it's 20 points that I could use. It's all or nothing. Also to mention, I KNOW there are 2 triangles that are isosceles to it has to be an isosceles proof/postulate. I performed the exercise twice in the image (with two different hut locations) to show that the treasure appeared in the same place. If you do it, be sure to use a straight edge and protractor for accurate results.




I apologize the image is on its side. ​