1. Why does the line y = x only have one slope? What is true about all of the triangles? How does this relate to Pythagorean Theorem?

2. Right Triangles Day 3 – Special Right Triangles

3. Answers to Homework 1) Yes, 12 + 15 > 20 2) No, 5 + 6 < 13 3) Yes, 2 + √7 > 4 4) 12 2 + 16 2 = 20 2 144 + 256 = 400 400 = 400 Right Triangle 5) (6 √3 ) 2 + (8 √3 ) 2 = (10 √3 ) 2 108 + 192 < 300 300 < 300 Right Triangle 6) ( √12 ) 2 + ( √21 ) 2 = (4 √2 ) 2 12 + 21 > 32 33> 32 Acute Triangle 7) 8 2 + 7 2 = 10 2 64 + 49 > 100 Acute Triangle 8) (4 √2 ) 2 + (4 √2 ) 2 = (8) 2 32 + 32 = 64 Right Triangle 9) 28 2 + 96 2 = 110 2 784 + 9216 < 12100 Obtuse Triangle 10) 59 2 + 60 2 = 80 2 3481 + 3600 > 6400 Acute Triangle

4. Answers to Homework 11) 12 2 + (12 √3 ) 2 = 24 2 144 + 432 = 576 Right Triangle 12) 5 2 + ( √60 ) 2 = 8 2 25 + 60 > 64 Acute Triangle 13) PR 2 + RQ 2 = PQ 2 ( √10 ) 2 + ( √20 ) 2 = ( √26 ) 2 10 + 20 > 26 Acute Triangle 14) (a) 2 + (b) 2 = (c) 2 (2n) 2 + (n 2 - 1) 2 = (n 2 + 1) 2 4n 2 + n 4 - 2 n 2 + 1 = n 4 + 2 n 2 + 1 2 n 2 + 1 = 2 n 2 + 1 Yes, this method will work because both sides of the equation are equal. 15) StatementsReasons 1. AB = 4, BC = 2, AC = √10 1. Given 2. AB 2 + AC 2 = BC 2 2. Pythagorean Theorem 3. 2 2 + ( √10) 2 = 4 2 3. Substitution 4. 14 < 164. Substitution 5.  ABC is an obtuse triangle 5. Pythagorean Theorem Converse 6.  ABC is acute angle 6. Definition of obtuse triangle 7.  1 is an acute angle 7. Vertical Angles are Congruent

5. Objective  To find the side length of special right triangles

6. Homework  Special Right Triangles Worksheet  Need help? Look in your book – Section 9.4

7. Special Right Triangles  Find the length of the hypotenuse

8. Isosceles Right Triangles 45 o Ratio of the sides in a 45:45:90 Right Triangle is 1: 1: √2

9. Find the lengths of the sides

11. Find the length of the sides Rule: NO RADICALS IN THE DENOMINATOR!!! Rationalize the denominator

12. Find the length of the sides Rule: NO RADICALS IN THE DENOMINATOR!!! Rationalize the denominator

13. 30-60-90 Triangles Equilateral Triangle 60 o 30 o 60 o 30 o 60 o

14. Isosceles Right Triangles Ratio of the sides in a 30:60:90 Right Triangle is 1: √3 : 2 30 o 60 o

15. Find the lengths of the sides

17. Solve for x.

18. Did you meet today’s objective?  How do special right triangles relate to Pythagorean Theorem?