Complete the following:

1. Complete the following: • Using the rectangular piece of paper on your desk: • Draw one diagonal from one vertex • Cut along the diagonal • Using one of your right triangles, draw an altitude from the right angle • Cut along the altitude…you should now have three triangles… • What can you say about the three triangles that you have? Measure the sides/angles if needed….

2. Chapter 9 Right Triangles Theorem: If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. C ∆CBD~ ∆ABC~ ∆ACD A B D

3. Geometric Mean Theorems • In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the lengths of the two segments. C AD/CD = CD/DB A B D

4. u • In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. • The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.

5. AB/AC = AC/AD • AB/CB = CB/DB C leg leg A B D

6. x 6 10 Examples • Find the value of each variable. 2 y 5

7. x 14 24 Examples 5 18 y

8. The Pythagorean Theorem! AGAIN!!! • In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. a²+ b² = c² c b a

9. Examples 6√5 x x 7 x 12 24 3/2 2

10. Pythagorean Triple? • Three positive integers (no fractions, decimals or square roots) that satisfy the pythagorean theorem. Is this a pythag. Triple? 5,12,13 3,4,5 1,1,√2

11. Area of a Triangle • A = ½ bh 8m 5cm 8m 10m 4cm

12. Complete assn #1 and #2 