Handout Geometry
-2857502286004200525247650Geometric Mean1647825340360When you wrote the proportionality statements, you used some segments twice. This is because the triangles overlapTo calculate the geometric mean of a set of numbers, multiply the numbers and take the nth root. If there are only two numbers in the set, take the square root of the product. Here is a definition that may help you see the relationship between the proportions you wrote and the geometric mean. x is the geometric mean of a and b if ax = xb , or x2= ab, or x =ab.Corollary - forming a proposition that follows from one already proved.3239770197485-186055197485-27622566675Using Pythagorean Theorem: a2 + b2 = c252 +122 = c2 25 +144 = c2 169 = c2 169 = c 13 = c or AC = 13 h2=x(y) h2=1.92(11.08) 52=x(13) 122= y(13) h2 = 21.272513 = 13x13 14413 = 13y13 h= 21.27 1.92 = x 11.08 = y h = 4.61-19050076835PRACTICE EXERCISES: Apply the concepts of geometric mean to answer the following problems:Find the geometric mean of 10 and 30. 4. Find the value of x, y and z.375285062230Find the value of x. 9525149225Find the value of y.9525028575Another example:190500211455Find the value of x and h in the given problem below: ................
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