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LESSON 8.4: Similarity in Right Triangles OBJECTIVES: To determine and use relationships in similar right triangles Vocabulary and Key Concepts The geometric mean of two positive numbers a and b is ________________________ the positive number m such that a m Example: Find the geometric mean of 4 & 16. = ____. m b If 4 =m m 16 , then m 2 = (4)(16) m 2 = 64 m=8 Thus, the geometric mean of 4 and 16 is 8. SV FINDING THE GEOMETRIC MEAN Find the geometric mean of 3 and 12. 3 =m m 12 m2 = 36 SV m =6 NOTE: We use only the positive square root, since length/distance is measured in positive numbers. 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 ___________________________________. Corollary 1 to 8-3: The length of the altitude to the hypotenuse of a right the geometric mean of the triangle is ________________________ lengths of the segments of the ________________________________ hypotenuse. ________________________________. Corollary 2 to 8-3: The altitude to the hypotenuse of a right triangle ________________________________ 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. 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. Work Space: 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? Homework Assignment: