1. 11/27/20158-2: Special Right Triangles1 G1.2.4: Prove and use the relationships among the side lengths and the angles of 30°- 60°- 90° triangles and 45°- 45°- 90° triangles. L1.1.6: Explain the importance of the irrational numbers √2 and √3 in basic right triangle trigonometry, the importance of π because of its role in circle relationships, and the role of e in applications such as continuously compounded interest.

2. 11/27/20158-2: Special Right Triangles2 Isosceles Right Triangles If a right triangle is isosceles, then it has 2 ___________ _________ and 2 ___________ __________. This means the measure of each acute angle must be ______. Thus another way to refer to Isosceles Right Triangles is as ___________ right triangles.

3. 11/27/20158-2: Special Right Triangles3 45 - 45 - 90 Right Triangles

4. 11/27/20158-2: Special Right Triangles4 The triangle below is an isosceles right triangle. What is the length of the hypotenuse? Calculate your answer 2 different ways. 6

5. 11/27/20158-2: Special Right Triangles5 If one leg of an isosceles right triangle measures 15 feet, what is the perimeter of the triangle?

6. 11/27/20158-2: Special Right Triangles6 What is the perimeter of the square?

7. In an isosceles right triangle, the hypotenuse is 12. What is the length of one (1) of the sides? A. B. C. D. E.

8. 11/27/20158-2: Special Right Triangles8 The largest triangle is equilateral and the segment in the interior is perpendicular to the base. Determine the values of x and y. 10 x y

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10. 11/27/20158-2: Special Right Triangles10 30 -60 - 90 Right Triangles When we cut an equilateral triangle with one altitude, we form 2 congruent right triangles each with one 30 and one 60 degree angle. These are called 30 - 60 - 90 right triangles.

11. 11/27/20158-2: Special Right Triangles11 30 - 60 - 90 Right Triangle Theorem If the shortest leg of a 30-60-90 right triangle is x units long, then the hypotenuse is 2x units long and the longer leg is x times the square root of 3 units long.

12. 30 – 60 – 90 Triangle 60° 30° x 2xx√3

13. 11/27/20158-2: Special Right Triangles13 Solve for x and y 60  18 x y

14. 11/27/20158-2: Special Right Triangles14 Solve for x and y 60° y x 24

15. 11/27/20158-2: Special Right Triangles15 Solve for x and y 60° y 34.64 x

16. 11/27/20158-2: Special Right Triangles 16 An altitude of an equilateral triangle is 8.3 meters. Find the perimeter of the triangle to the nearest tenth of a meter.

17. 11/27/20158-2: Special Right Triangles17 Assignment Pages 409 - 410, # 11 - 21 (odds), 33