In addition to the length of the altitude being the geometric mean of the lengths of the two hypotenuse segments, there are additional ratios created by the three similar right triangles. In this section, you will investigate relationships between the lengths of the legs and the hypotenuse segments.
For this, we will need to know a few more vocabulary terms:
In the figure above the altitude creates two similar triangles, the red triangle, ∆ABD, is similar to the blue triangle, ∆BCD. Since they are similar they have similar ratios.
Right Similar Triangles Applet
What patterns do you notice?
Answer the following in your notes: