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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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© 2008 Pearson Addison-Wesley. All rights reserved 9-4-1 Chapter 1 Section 9-4 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem.

© 2008 Pearson Addison-Wesley. All rights reserved 9-4-1 Chapter 1 Section 9-4 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem.

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