📐 Topic Summary
When an altitude is drawn from the right angle of a right triangle to its hypotenuse, it creates two smaller triangles that are similar to each other and to the original triangle. This similarity allows us to set up proportions to find the lengths of missing sides. Remember the altitude is the geometric mean between the two segments of the hypotenuse. Each leg of the original right triangle is the geometric mean between the hypotenuse and the segment of the hypotenuse adjacent to that leg.
This property gives us three important relationships:
- 📏 The altitude's length is the geometric mean of the two segments it creates on the hypotenuse.
- 💡 Each leg's length is the geometric mean of the entire hypotenuse and the segment of the hypotenuse adjacent to that leg.
🧮 Part A: Vocabulary
Match the term with its definition.
- Altitude
- Hypotenuse
- Leg
- Similar Triangles
- Geometric Mean
- The side opposite the right angle in a right triangle.
- A line segment from a vertex of a triangle perpendicular to the opposite side.
- Triangles that have the same shape but different sizes.
- One of the two sides that form the right angle in a right triangle.
- The square root of the product of two numbers.
✍️ Part B: Fill in the Blanks
When an ________ is drawn from the right angle of a right triangle to its ________, it creates two smaller triangles that are ________ to each other and to the original triangle. The ________ is the geometric mean between the two segments of the hypotenuse.
🤔 Part C: Critical Thinking
Explain how the altitude to the hypotenuse theorem can be used in real-world applications, providing a specific example.