6.8Similarity in Right Triangles
Quick Answer
The altitude to the hypotenuse of a right triangle creates two smaller triangles that are similar to each other and to the original. This gives the geometric mean relationships: altitude² = (segment 1)(segment 2) and leg² = (hypotenuse)(adjacent segment).
Essential Question
How does the altitude to the hypotenuse of a right triangle create three similar triangles, and what geometric mean relationships does this produce?
Learning Goals
- 1Identify the three similar triangles formed by the altitude to the hypotenuse.
- 2Apply the geometric mean (altitude) relationship.
- 3Apply the geometric mean (leg) relationship.
- 4Solve problems using right triangle similarity.
Key Vocabulary
Geometric mean
For positive numbers a and b, the geometric mean is √(ab).
Altitude to the hypotenuse
The segment from the right angle vertex perpendicular to the hypotenuse, which creates two similar triangles.
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.