GEOM.MATH.8.B
Identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems.
Geometry · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012
Standard Unwrapping
AI-generated as a starting point — sign in to edit.Vocabulary
relationshipsaltitudehypotenuseright trianglegeometric meanproblems
Skills
- identify (relationships when an altitude is drawn to the hypotenuse of a right triangle) #dok2
- apply (relationships involving the geometric mean in right triangles) #dok3
- solve (problems using properties of altitudes drawn to hypotenuses in right triangles) #dok3
Learning Targets
- I can locate the altitude drawn to the hypotenuse in a right triangle. #dok1
- I can define the geometric mean in the context of right triangles. #dok1
- I can identify the relationships created by the altitude drawn to the hypotenuse of a right triangle. #dok2
- I can represent the geometric mean relationships using equations. #dok2
- I can apply geometric mean properties to solve for missing segment lengths in right triangles. #dok3
- I can solve real-world and mathematical problems involving right triangles and geometric mean relationships. #dok3
Big Ideas
- Drawing an altitude to the hypotenuse of a right triangle creates similar triangles, establishing specific proportional relationships known as geometric means.
- Understanding and applying the geometric mean relationships helps solve complex problems involving segments in right triangles.
Essential Questions
- What happens to a right triangle when an altitude is drawn to its hypotenuse?
- How are the smaller triangles formed by the altitude similar to the original triangle?
- What is the geometric mean, and how does it relate to the segments in a right triangle?
- How can understanding these relationships help solve for unknown lengths in right triangles?
- In what types of real-world problems might you use the geometric mean relationships of right triangles?