8-1 – Similarity in Right Triangles

1. 8-1 – Similarity in Right Triangles Objective: Determine the geometric mean between two numbers. Apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle.

2. If a, b, and x are positive numbers and , then x is the ___________________ __________ between a and b. • Notice x is both ___________ in the proportion. Geometric Mean

3. Find the geometric mean between the two numbers. • 5 and 20 • 1 and 3 Examples

4. Answer questions 1-3

5. If the ________________ is drawn to the hypotenuse of a right triangle, then the two triangles formed are _______________ to the original triangle and each other. • Example: Y Similarity in Right Triangles X A Z

6. Answer question 4

7. When the altitude is drawn to the hypotenuse of a right triangle, • the length of the altitude is the _______________ __________ between the segments of the hypotenuse. • each leg is the _______________ __________ between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg. • Examples: For leg : For leg : Y } Similarity in Right Triangles X A Z

8. If and , find . • If and , find . • If and , find . • If and , find . C Examples A N B

9. Answer questions 5-8