1. Metric Relations in Right Triangles

2. Lesson 1 Take the following 2 pages of notes
Create a triangle and proof the triangles are similar after adding an altitude
Work in Visions textbook 1 page 179

3. By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C
△ABC∼△ACD∼△ADB

4. Reminder: Similar Triangles
Corresponding angles are congruent
AND
Corresponding sides are proportional in length
Minimum Conditions: AA
SAS
SSS

5. 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

6. Class work and Homework
Activity 1: Birds of a feather stick together!

7. Lesson 2 Finish and correct Birds of a feather
Everyone create a triangle as on next slide and write in the names of each part of the triangle created

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

9. Everyone draw another right angle triangle and name it
Add the altitude
Label all parts of the triangles created

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

11. Property 1 Information we have or need: 1. Measurement of leg
2. Measurement of projection
3. Measurement of hypotenuse

12. Property 1:
leg
leg
proj
proj

13. Property 1:
leg
leg
proj
proj

14. Class work and homework
Worksheet hand out on Property 1

15. Lesson 3
Correct work on property 1

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

17. Property 2:
altitude
proj
proj

18. Class work and Homework
Worksheet on Property 2

19. Lesson 4

20. Property 3 Information we have or need: 1. Hypotenuse 2. Altitude
3. Length of legs

21. Property 3:
leg
leg
altitude
hypotenuse

22. Property 3: Textbook Definition and formula
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.

23. Class work and homework
Hand out on property 3

24. Lesson 5 Correct all homework Go over the information to date
Draw and altitude within a right triangle
Label the parts
Write the properties What is property 4? You already know it!!!

25. Property 4 You already know it: Pythagorean theorem
leg² + leg² = hypotenuse²

26. Class Work and Homework
Visions page 182, numbers 1,2,3,4