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9.3 Altitude-On-Hypotenuse Theorems (a.k.a Geometry Mean) When an altitude is drawn from to a hypotenuse then three similar triangles are formed. Identify the three similar triangles! Which theorem can they be proven similar? Remember: Given two numbers a and b, x is the geometric mean if EXTREMES MEANS a x x b Find the geometric mean of 9 and 16 a x x b 9 x x 16 x 144 2 x 12 Altitudes!!!! What do you remember? C A D B An Altitude *Starts at a vertex *Forms a right angle The hypotenuse is split into two pieces BD and DA C A D B CD (the altitude) is the geometric mean of those two pieces If the altitude is in the means place, put the two segments of the hypotenuse into the extremes. C A D B 1st piece hyp altitude altitude 2nd piece hyp If the leg is in the means place, put the whole hyp. and segment closest to that leg into the extremes. A whole hyp leg D leg side close to leg the LEG is the geometric mean AB AC C B AC AD A whole hyp leg leg side close to leg D AB CB C the LEG is the geometric mean B CB BD EX: 1 Find x C A x 9 16 D 9 B x x 16 x 144 2 x 12 EX: 2 Find the length of AB. A 15 D 32 1024 68.26 x 15 C B EX 3: Solve for x C A 4 x D 3 B 16 x 5.33 3 EX: 4 Find the length of CB. A 50 D 32 x = 40 C x B EX: 5 Solve for x C A 5 12 D x B 25 x 2.08 12