Proportions in Right Triangles

1. Proportions in Right Triangles Theorem 7.1 • The altitude to the hypotenuse of a right triangle forms two triangles similar to it and each other. ABC~ADB ~ BDC

2. Proportions in Right Triangles Geometric mean – For two positive numbers a and b, the geometric mean is the positive number x where the proportion a/x = x/b is true. In other words, x = ab.

3. Example 1-1c a. Find the geometric mean between 3 and 12. b. Find the geometric mean between 4 and 20. Answer: 6 Answer: 8.9

4. Proportions in Right Triangles Theorem 7.2 • The altitude to the hypotenuse of a right triangle is the geometric mean between the segments into which it divides the hypotenuse. AD:BD = BD:CD Theorem 7.3 • Each leg of a right triangle is the geometric mean between the hypotenuse and its projection on the hypotenuse. AC:AB = AB:AD AC:BC = BC:DC

5. Example 1-2c Answer: about 8.5

6. f Answer: Example 1-4d Find e and f.

7. AIRPLANES A jetliner has a wingspan, BD, of 211 feet. The segment drawn from the front of the plane to the tail, intersects at point E. If AE is 163 feet, what is the length of the aircraft? Example 1-3d Answer: about 231.3 ft