1. Geometry Warm-Up1/31/12  Find the value of x. 13 7 x x 12 15 1. 2.

2. Perfect Squares Quiz 12. 14 2 2. 17 2 3. 12 2 4. 5 2 5. 8 2 6. 19 2 7. 11 2 8. 1 2 9. 20 2 10. 16 2 11. 7 2 1. 4 2 13. 2 2 14. 10 2 15. 3 2 16. 18 2 17. 13 2 18. 9 2 19. 15 2 20. 6 2

3. Sec 8.3: Special Right Triangles Geometry January 31, 2012

4. Special Right Triangles  Special Right Triangles Triangles whose angles measures are either 45  -45  -90  or 30  -60  -90 .

5. 45  -45  -90  Triangle  Special Relationships Because you have two 45  angles, the two legs are congruent. The hypotenuse is √2 times as long as each leg  Hypotenuse = √2 ● leg

6. 30  -60  -90  Triangles  Special Relationships Because the two acute angles have different measures, you have a long leg and a short leg The hypotenuse is twice as long as the short leg and the long leg is √3 times as long as the short leg.  Hypotenuse = 2 ● short leg  Long Leg = √3 ● short leg

7. Example 1  Find the value of x. Hypotenuse = √2 ● leg x = √2 (7) x = 7√2

8. Example 2  Find the values of s and t. Long leg = √3 ● short leg 9 = √3 (s) 9√3 = s 3 3√3 = s Hyp = 2 ● short leg t = 2 (3√3) t = 6√3