1. Geometry Chapter 8 Review

2. Geometric Mean Find the geometric mean between the two numbers. 7.5 and 20 8.64 and 49

3. Corollary 1 piece of hypotenuse altitude altitude other piece of hypotenuse Y AZ X =

4. Corollary 2 hypotenuse leg leg piece of hyp. adj. to leg Y AZ X =

5. Corollary 2 Y AZ X hypotenuse leg leg piece of hyp. adj. to leg =

6. Pythagorean Theorem In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. a b c C A B

7. If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. Theorem: Converse of the Pythagorean Theorem a b c If c² = a² + b²Rt. ∆

8. If the square of the longest side of a triangle is greater than the sum of the squares of the other two sides, then the triangle is an obtuse triangle. Theorem a b c If c² > a² + b² Obtuse ∆ obtuse

9. If the square of the longest side of a triangle is less than the sum of the squares of the other two sides, then the triangle is an acute triangle. Theorem a b c If c² < a² + b² Acute ∆ acute

10. 45-45-90 Triangles 45 o o x x Since all 45-45-90 triangles are similar, by AA Similarity Postulate, this formula works for all 45-45-90 triangles. The formula.

11. 30-60-90 Triangles 60 o 30 o x 2x Since all 30-60-90 triangles are similar, by AA Similarity Postulate, this formula works for all 30-60-90 triangles. The formula.

12. Tangent ratio = opposite leg adjacent leg hypotenuse A Tangent of <A: The tangent ratio is the ratio of the length of the legs in a Rt. ∆

13. Sine and Cosine Ratios opposite leg adjacent leg hypotenuse A Sine of <A: The sine ratio is the ratio of the length of the legs in a Rt. ∆ opposite leg adjacent leg hypotenuse A Cosine of <A:

14. HW  W.S. Let’s do the odds on Chapter 8 side together!