What has been your most effective method for teaching to solve for two missing sides of a 45-45-90 and a 30-60-90? I have found that teaching it with formulas like a, a(root2) and a, a(root3), and 2a tends to confuse many kids due to introducing a third variable (in the formulas) when often there are already two variables in a diagram. I have tried teaching it through words or rules. Ex: “the medium side is equal to the short side times root(3).” Kids tend to just forget these rules or mix them up. Eventually, I have settled on simply teaching the 1:1:root(2) ratio and the 1:root(3):2 ratio for side lengths, and then the kids set up proportions using these and the corresponding values from the diagram. It is more mechanical than other intuitive approaches, but I think the kids who excel with the intuitive approaches will find their own mental or visual shortcuts anyway. The only thing I dislike about this is that it can take longer than more intuitive approaches. But, just making up numbers here, 80% of kids doing it successfully in a longer way is better than 60% doing it correctly in a shorter way. We will see what the data says come assessment time. What have been other math teachers’ experiences with this topic and the various ways to teach it?