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

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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

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Sec 8.3: Special Right Triangles Geometry January 31, 2012

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

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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

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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

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

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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

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