1. LESSON 8.4: Similarity in Right Triangles OBJECTIVES: To determine and use relationships in similar right triangles

2. Vocabulary and Key Concepts The geometric mean of two positive numbers a and b is ________________________ ____. the positive number m such that If, then m 2 = (4)(16) m 2 = 64 m = 8 SV Thus, the geometric mean of 4 and 16 is 8. Example: Find the geometric mean of 4 & 16.

3. FINDING THE GEOMETRIC MEAN Find the geometric mean of 3 and 12. m 2 = 36 NOTE: We use only the positive square root, since length/distance is measured in positive numbers. m = 6 SV

4. Theorem 8-3: The altitude (perpendicular segment) to the hypotenuse of a right triangle ___________________________________ ___________________________________ ___________________________________. divides the triangle into two triangles that are similar to the original triangle and to each other

5. Corollary 1 to 8-3: The length of the altitude to the hypotenuse of a right triangle is ________________________ ________________________________ ________________________________. Corollary 2 to 8-3: The altitude to the hypotenuse of a right triangle ________________________________ ________________________________ ________________________________ ________________________________ ________________________________. the geometric mean of the lengths of the segments of the hypotenuse. separates the hypotenuse so that the length of each leg of a triangle is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse.

6. FINDING DISTANCE At a golf course, Maria Teehawk drover her ball 192 yards straight toward the cup. Her brother, G.O. Teehawk drove his ball 240 yard, but not toward the cup. The diagram shows the results. Find x and y, their remaining distances from the cup. Next, find the distance between Maria’s ball and G.0.’s ball.

7. Work Space:

8. Final Checks for Understanding 1.How can we use relationships in similar right triangles in real-life? 2.What is the geometric mean of two numbers? 3.Find the geometric mean of 15 and 20. 4.Why do we use only the positive square root when finding the geometric mean of two numbers?

9. Homework Assignment: