Download 4) Write the similarity statement comparing the three triangles

Notes: 8.1 Geometric mean If we consider the proportion ax = xb you will notice that the means of the proportions are the same number. That number is the geometric mean of the extremes. Geometric Mean – given two numbers “a” and “b”, use the following formula to find the geometric mean “x”. 1) Find the geometric mean of 2 and 8. 2) Find the geometric mean of 4 and 5. 3) If one number is 6 and the geometric mean of the two numbers is 4. What is the other number? Theorem 8­1­1 If the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the two triangles formed are similar to the given triangle and each other. (3 Similar triangles formed) 4) Write the similarity statement comparing the three triangles ​△​______​~△​______​~△​______ ___________________________________________________________________________________ Geometric Mean 8­1­2 The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean​ between the measures of the two segments of the hypotenuse. P art 1
altitude
= altitude
P art 2 find x: 5) 6) _________________________________________________________________________________________________
_ Geometric Mean 8­1­3 If the altitude is drawn to the hypotenuse of a right triangle, then the measures of a leg of the triangle is the geometric mean between the measures of the hypotenuse and the segment of the hypotenuse adjacent to the leg. whole hypotenuse
leg 1
whole hypotenuse
leg 2
leg 1
= part 1
leg 2
= part 2
Find x and y: 7) 8) 9) 10)