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**Aim: What’s so special about a 300-600-900 triangle?**

Do Now: Triangle ABC is equilateral with each side equal to 2x. CD is an altitude of ABC. What is mA? mB? mACB? What is mACD? mBCD? 600 C 300 2x 2x A B D 2x

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**Pythagorean Theorem - a2 + b2 = c2**

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? C 300 2x 2x Pythagorean Theorem - a2 + b2 = c2 ? A 600 B x 2x D x2 + (CD)2 = (2x)2 x2 + (CD)2 = 4x2 (CD)2 = 3x2

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**Pythagorean Theorem - a2 + b2 = c2**

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? C 300 Pythagorean Theorem - a2 + b2 = c2 6 6 ? A 600 B 32 + (CD)2 = (6)2 3 D 9 + (CD)2 = 36 (CD)2 = 27

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**Review the results of the first two problems. **

triangle Problem 1 Problem 2 A 6 3 C D A C 2x x D 3 300 300 600 600 Review the results of the first two problems. Can you make any general conclusions?

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triangle 300 2s 600 s

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**Pythagorean Theorem - a2 + b2 = c2**

45o - 45o - 90o triangle Triangle ABC is an isosceles right triangle with BC = A. What is mB? mC? AB? AC? Do Now: C 450 x 2 A B Pythagorean Theorem - a2 + b2 = c2 x2 + x2 = ( )2 2x = ( )2 2x = 8

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**Pythagorean Theorem - a2 + b2 = c2**

45o - 45o - 90o triangle Triangle ABC is an isosceles right triangle with BC = A. What AB? AC? Do Now: 2 6 6 C 2 6 x A B Pythagorean Theorem - a2 + b2 = c2 x2 + x2 = ( )2 2 6 2x = 72 x = 36 x = 6

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**Review the results of the first two problems. **

triangle Problem 1 Problem 2 C C 2 6 A B A B Review the results of the first two problems. Can you make any general conclusions?

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triangle In a triangle, the length of the hypotenuse is times the length of a leg. 450 s 450 s Ratio of Hypotenuse : Leg of I.R.T is always

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**Isosceles Right Triangle**

BF AB = = 2 450 CG AC = = 2 DH AD = = 2 EI AE = = 2 Ratio of Hypotenuse : Leg of I.R.T is always

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**Summary of Special Angles in Trig**

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**Triangle ABC is a 30-60-90 triangle with BC = 7 A. What is length of **

Model Problem Triangle ABC is a triangle with BC = 7 A. What is length of AB? AC? Do Now: C 300 7 3.5 A 600 B 3.5 Hypotenuse is 2 times the shorter leg CB = 2(AB) 7 = 2(AB) 3.5 = AB Longer leg is times the shorter leg AC = (AB) 3 AC = (3.5) 3 AC 6.06

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**Pythagorean Theorem - a2 + b2 = c2**

Model Problem Triangle ABC is an isosceles right triangle with BC = 8 A. What AB? AC? Do Now: C 8 x A B Ratio of Hypotenuse : Leg of I.R.T is always Pythagorean Theorem - a2 + b2 = c2 x2 + x2 = (8)2 2x = 64 x = x = 32 2 4 Instead of

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Regents Prep What is the exact sum of + 0

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Model Problem The rhombus below is a glass panel for a door. How many square inches of colored glass will you need for the panel? A = bh 6 in. 600 Draw an altitude of the rhombus. Label x and h as shown x h 6 in. 6 in. 600 Hypotenuse is 2 times the shorter leg 6 = 2x 3 = x Longer leg is times the shorter leg A = bh = 6( ) = 31.2 in2 h =

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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? hypotenuse is times the length of a leg. 2 90’ Isosceles Right Triangle 90’ 90 = ’ 2

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The Pythagorean Theorem. Pythagoras Lived in southern Italy during the sixth century B.C. Considered the first true mathematician Used mathematics as.

The Pythagorean Theorem. Pythagoras Lived in southern Italy during the sixth century B.C. Considered the first true mathematician Used mathematics as.

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