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Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig. Aim: Whats so special about a triangle? Do Now: Triangle ABC is equilateral with each side equal to 2x. CD is an altitude of ABC. What is m A? m B? m ACB? What is m ACD? m BCD? AB C 2x2x 2x2x 2x2x D

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Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig triangle Triangle ABC is equilateral with each side equal to 2x. CD is an altitude of ABC What is length of CD in terms of x? AB C 2x2x 2x2x 2x2x ? Pythagorean Theorem - a 2 + b 2 = c 2 x 2 + (CD) 2 = (2x) 2 (CD) 2 = 3x 2 xx x 2 + (CD) 2 = 4x 2 D

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Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig triangle Triangle ABC is equilateral with each side equal to 6 (instead of 2x). CD is an altitude of ABC What is length of CD? AB C 6 6 ? Pythagorean Theorem - a 2 + b 2 = c (CD) 2 = (6) 2 (CD) 2 = (CD) 2 = 36 D

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Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig triangle A C 2x2x x D 3 x A C D Review the results of the first two problems. Can you make any general conclusions? Problem 1 Problem

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Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig triangle s 2s2s

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Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig. 45 o - 45 o - 90 o triangle Do Now: Triangle ABC is an isosceles right triangle with BC = A. What is m B? m C? AB? AC? AB C 45 0 Pythagorean Theorem - a 2 + b 2 = c 2 x x x 2 + x 2 = ( ) 2 2x 2 = ( ) 2 2x 2 = 8 2 2

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Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig. 45 o - 45 o - 90 o triangle Do Now: Triangle ABC is an isosceles right triangle with BC = A. What AB? AC? AB C Pythagorean Theorem - a 2 + b 2 = c 2 x x x 2 + x 2 = ( ) 2 2x 2 = 72 x 2 = 36 x =

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Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig triangle Review the results of the first two problems. Can you make any general conclusions? Problem 1 Problem 2 AB C 2 2 AB C 6 6

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Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig triangle s In a triangle, the length of the hypotenuse is times the length of a leg s Ratio of Hypotenuse : Leg of I.R.T is always

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Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig. Isosceles Right Triangle 45 0 – triangle BF AB = = 2 CG AC = = 2 DH AD = = 2 EI AE = = Ratio of Hypotenuse : Leg of I.R.T is always

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Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig. Summary of Special Angles in Trig

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Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig. Model Problem Do Now: Triangle ABC is a triangle with BC = 7 A. What is length of AB? AC? AB C Hypotenuse is 2 times the shorter leg CB = 2(AB)7 = 2(AB) Longer leg is times the shorter leg AC = (AB) 3 AC 6.06 AC = (3.5) = AB 3.5

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Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig. Model Problem Do Now: Triangle ABC is an isosceles right triangle with BC = 8 A. What AB? AC? AB C x x 8 Pythagorean Theorem - a 2 + b 2 = c 2 x 2 + x 2 = (8) 2 2x 2 = 64 x 2 = 32 x = x = Instead of Ratio of Hypotenuse : Leg of I.R.T is always

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Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig. Regents Prep What is the exact sum of + 0

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Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig. The rhombus below is a glass panel for a door. How many square inches of colored glass will you need for the panel? Model Problem 6 in in. Draw an altitude of the rhombus. Label x and h as shown x h 6 = 2x Hypotenuse is 2 times the shorter leg 3 = x h = Longer leg is times the shorter leg A = bh = 6( ) = 31.2 in 2 A = bh

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Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig. Model Problem A baseball diamond is a square. The distance from base to base is 90 ft. To the nearest foot, how far does the second baseman throw a ball to home plate? 90 Isosceles Right Triangle 90 = hypotenuse is times the length of a leg.2

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