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9.3 Altitude-On-Hypotenuse Theorems (a.k.a Geometry Mean)

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?.

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9.3 Altitude-On-Hypotenuse Theorems (a.k.a Geometry Mean)

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  1. 9.3Altitude-On-Hypotenuse Theorems (a.k.a Geometry Mean)

  2. 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?

  3. Remember: Given two numbers a and b, x is the geometric mean if EXTREMES MEANS

  4. Find the geometric mean of 9 and 16

  5. Altitudes!!!! What do you remember? C A An Altitude *Starts at a vertex *Forms a right angle D B

  6. The hypotenuse is split into two pieces BD and DA C A CD (the altitude) is the geometric mean of those two pieces D B

  7. If the altitude is in the means place, put the two segments of the hypotenuse into the extremes. C A D B

  8. If the leg is in the means place, put the whole hyp. and segment closest to that leg into the extremes. A D the LEG is the geometric mean AB AC AC AD C B

  9. A D AB CB CB BD C B the LEG is the geometric mean

  10. EX: 1 Find x C A x 9 x 16 x 16 D 9 B

  11. EX: 2 Find the length of AB. A 15 D 32 C B

  12. EX 3: Solve for x C A 4 x D 3 B

  13. EX: 4 Find the length of CB. A 50 D 32 x = 40 B C x

  14. EX: 5 Solve for x C A 5 12 D x B

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