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8-2: Special Right Triangles 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. 5/24/2017 8-2: Special Right Triangles 1 You have 1 minute to get ready for the quiz. Daily Quiz 5/5/2011 Determine the perimeter of the triangle below. 32 x 3x 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. 5/24/2017 8-2: Special Right Triangles 4 Isosceles Right Triangle Theorem If each leg of an isosceles right triangle is x units long, then the hypotenuse is xtimes the square root of 2 units long. 45 - 45 - 90 Right Triangles 5/24/2017 8-2: Special Right Triangles 6 The triangle below is an isosceles right triangle. What is the length of the hypotenuse? Calculate your answer 2 different ways. 6 5/24/2017 8-2: Special Right Triangles 7 DQ 5/6/2011 An isosceles triangle has perimeter of 34.1421 feet. What is the length of the hypotenuse of the triangle? If one leg of an isosceles right triangle measures 15 feet, what is the perimeter of the triangle? 5/24/2017 8-2: Special Right Triangles 13 What is the perimeter of the square? Class work – 2pts 2 minutes 8 2 5/24/2017 8-2: Special Right Triangles 14 In an isosceles right triangle, the hypotenuse is 12. What is the length of one (1) of the sides? A. 6 2 B. 2 6 C. 2 4 D. 2 3 E. 3 Class work – 2pts 3 minutes The largest triangle is equilateral and the segment in the interior 10 is perpendicular to the base. Determine the values of x x and y. y 5/24/2017 8-2: Special Right Triangles 16 5/24/2017 8-2: Special Right Triangles 17 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. 5/24/2017 8-2: Special Right Triangles 18 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. 5/24/2017 8-2: Special Right Triangles 19 30 – 60 – 90 Triangle 30° x√3 2x 60° x Solve for x and y x y 60 18 5/24/2017 8-2: Special Right Triangles 21 Solve for x and y x 24 60 ° y 5/24/2017 8-2: Special Right Triangles 22 Solve for x and y 34.64 x 60 ° y 5/24/2017 8-2: Special Right Triangles 23 An altitude of an equilateral triangle is 8.3 meters. Find the perimeter of the triangle to the nearest tenth of a meter. 5/24/2017 8-2: Special Right Triangles 24 Assignment Pages 409 - 410, # 11 - 21 (odds), 33 5/24/2017 8-2: Special Right Triangles 25