An envelope is drawn as a rectangle with lines from both top corners to the middle of the bottom edge, and one diagonal from the bottom-left corner to the top-right corner. How many triangles are in the figure?

Sort them by size. Small: the piece at the top between the two flap lines and the diagonal, 1, and the two pieces next to it, 2. Then 3 triangles of the next size, 1 larger and 3 of the largest size (each using a full side of the rectangle): $1+2+3+1+3=10$.