Right triangle ABC can be divided up into two smaller right triangles by drawing the altitude. You can move it around by dragging A up and down, or moving point M (the midpoint of the hypoteneuse).

By moving the sliders, one can see that two small triangles are similar. Is this true in all cases? Explain your response.
The two ratios of sides also appear the same. Is this true in all cases? Explain your response.
Calculate the area of the triangle in two different ways. Do you get the same answer?
Extension: Find another triangle which is similar to the first two. Why is it similar?