To teach the children about triangles, I began reading the book, "The Very Greedy Traingle." This is a wonderful book for both its math and literary qualities, and can be shared with children of any age! Then, we looked for triangles on the chart, and more importantly, talked about how we know it's a triangle. (You can see that we counted the sides and angles of each triangle.)
Then, the students got a bag of shapes (Tangrams, specifically) and sorted triangles and not-triangles. Finally, the students worked to compose shapes using the triangles. They found that they could build bigger triangles, squares, diamonds, and even a rectangle!