2.  By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

3.  Corresponding angles are congruent AND  Corresponding sides are proportional in length  Minimum Conditions: 1. AA 2. SAS 3. SSS

4. Activity Take 10 minutes. Use graph paper Draw a right triangle Draw the altitude from the right angle Prove that 3 similar triangles are formed

5.  Activity 1: Birds of a feather stick together!  Problem: Mother Nature Enraged!

6.  The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle. leg projection leg projection

7.  Using the lengths of the corresponding sides of the triangles formed, we can determine the ratios and from this determine certain geometric properties

8.  Information we have or need: 1. Measurement of leg 2. Measurement of projection 3. Measurement of hypotenuse

9. leg proj leg proj

10. leg proj leg proj

11.  In a right triangle the length of the leg of a right triangle is the geometric mean between the length of its projection on the hypotenuse

12.  Worksheet hand out on Property 1

13.  Information we have or need: 1. Altitude 2. 2 segments that determine hypotenuse i.e. projections

14. proj altitude

15.  In a right triangle the length of the altitude drawn from the right angle is the geometric mean of the length of the two segments that determine the hypotenuse

16.  Worksheet on Property 2

17.  Information we have or need: 1. Hypotenuse 2. Altitude 3. Length of legs

18. leg hypotenuse altitude

19.  In a right triangle, the product of the length of the hypotenuse and its corresponding altitude is equal to the product of the lengths of the legs.

20.  Hand out on property 3

21.  Pythagorean Theorem

22.  Visions page 182, numbers 1,2,3,4

23.  Each leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse.  or

24.  The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.