1. Congruence in Right Triangles
Geometry 4-6

2. Right Triangle Congruence
So, SSA is a bad congruence.
Are there any situations where it would still work?
Specifically, is there a given angle where SSA can only construct one triangle?
Right Triangle Congruence

3. Right Triangle Congruence
Supplies
Spaghetti (two small pieces)
Right Triangle Congruence

4. Right Triangle Congruence
On a piece of paper, draw a line and arrange your spaghetti as shown.
Long Piece
Short Piece
Right Triangle Congruence

5. Right Triangle Congruence
Long piece of spaghetti with a constant angle to the line.
Keep This angle constant
Right Triangle Congruence

6. Right Triangle Congruence
Move the short piece to form two different triangles, this is why SSA is not a good congruence
Right Triangle Congruence

7. Right Triangle Congruence
When does it form NO triangles, and more importantly, when does it form ONE triangle
Right Triangle Congruence

8. Right Triangle Congruence
No triangles when the short piece does not reach to the line
Right Triangle Congruence

9. Right Triangle Congruence
One triangle when the short piece just reaches to the line
What must this angle be when it just reaches?
Right Triangle Congruence

10. Right Triangle Congruence
At that point, we don’t need the first angle any more, and we still have a SSA triangle, with the right angle.
Right Triangle Congruence

11. Right Triangle Congruence

12. Right Triangle Congruence

13. Right Triangle Congruence

14. Right Triangle Congruence

15. Right Triangle Congruence

16. Practice

17. Practice

18. Practice

19. Practice

20. Practice

21. Practice

22. Practice

23. Practice

24. Practice

25. Pages 219 – 223
5 – 8, 11, 19, 20,
Homework

26. Pages 219 – 223
5 – 8, 11, 19, 20, 32,
Honors Homework