The student can use the geometric mean to find segment lengths in right triangles and apply similarity relationships to solve problems. Specifically: - The altitude to the hypotenuse of a right triangle forms two triangles similar to each other and the original triangle. Proportions can be set up between corresponding sides. - The length of the altitude to the hypotenuse is the geometric mean of the lengths of the two segments it forms. - The length of a leg is the geometric mean of the lengths of the hypotenuse and the adjacent segment. Setting up similar triangles allows solving for unknown lengths.