7.4Geometric Mean in Right Triangles
Quick Answer
When the altitude is drawn to the hypotenuse of a right triangle: altitude² = (segment 1)(segment 2); each leg² = (hypotenuse)(adjacent segment). These are the geometric mean relationships.
Essential Question
How do the geometric mean relationships in a right triangle follow from the three similar triangles created by the altitude to the hypotenuse?
Learning Goals
- 1Identify the three similar triangles formed by the altitude to the hypotenuse.
- 2Apply the geometric mean altitude theorem.
- 3Apply the geometric mean leg theorem.
- 4Solve for missing lengths using geometric mean.
Key Vocabulary
Geometric mean altitude theorem
altitude² = (hyp. segment 1)(hyp. segment 2).
Geometric mean leg theorem
leg² = (whole hypotenuse)(adjacent hypotenuse segment).
Full lesson content coming soon
Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.