Chapter 8 Section 1 Similarity in Right Triangles

Chapter 8 Section 1 (Similarity in Right Triangles) Recall the rules for simplifying radicals: 1. No perfect square factor other than 1 is allowed under the radical sign 2. No fraction is under the radical sign 3. No fraction has a radical in its denominator

Simplify these radicals:

Simplify these radicals:

Recall our general proportion: b & c are the means 1. If the means happen to be the same number… 2. That number is known as the geometric mean of a and d. (If a, d, and x are all positive).

Examples: Find the geometric mean between 4 and 25 As a proportion it will look like… Solving results in…

When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the segments of the hypotenuse. a b

When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the piece of the hypotenuse attached to it. a b c

When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the piece of the hypotenuse attached to it. c a leg 1 a b c

When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the piece of the hypotenuse attached to it. c c a leg 2 leg 1 a b c b

Ex. h H y E x 9 J 16 x x 2 = 144 x = 12 z 16 y 9 R 25 y y 2 = 225 y = 15 z 25 16 z z 2 = 400 z = 20

Ex. i H y E 2 x z 2 x J 4 2 4 x = 4 x= 1 4 R y 1 5 y y 2 = 5 y= z 4 5 z z 2 = 20 z=

Ex. j x y x+7 12 z

Chapter 8 Section 1 (Similarity in Right Triangles) Homework: Section 8. 1 Written Exercises #1– 39 (odds) (exact answers only)