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7.3 Notes Name____________________ Similar Right Triangles and Geometric Mean In the picture below are 3 similar triangles. Draw the 3 triangles separately and mark the corresponding parts. Then, complete the proportions. Δ ABC (big triangle) Δ ABD (left triangle) Δ CBD (right triangle) #1 Compare !CBD to !ABD #2 Compare !ABD to !ABC #3 Compare !CBD to !ABC AD AD CD BD = CB = CD AB = BC = AC = BC The geometric mean of two numbers is the number x that satisfies a x = AB x b = AC such that ab = x 2 . In the figure above, the following are geometric means: • BD (the altitude) is the geometric mean between ____________ and ____________ • AB (left leg) is the geometric mean between ____________ and ____________ • BC (right leg) is the geometric mean between ____________ and ____________ Altitude Geometric Mean (Heartbeat): In a Leg Geometric Mean (Boomerang): In a right right triangle, the length of the altitude from triangle, with an altitude drawn from right the right angle is the geometric mean between angle, the length of each leg is the geometric the two segments that form the hypotenuse. mean between the whole hypotenuse and the segment of the hypotenuse that is adjacent to the given leg. Find the exact value of the given variables. 1. Find a. 3. Find w. 5. Find AC and DB. 2. Find x. 4. Find AD.