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Geometry

Geometry. 8.4 Special Right Triangles This is a very important section, as it is used extensively throughout the second semester. 45-45-90 Triangles. The formula. o. 45. x. o. 45. x. Since all 45-45-90 triangles are similar, by AA Similarity Postulate,

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Geometry

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  1. Geometry 8.4 Special Right Triangles This is a very important section, as it is used extensively throughout the second semester.

  2. 45-45-90 Triangles The formula. o 45 x o 45 x Since all 45-45-90 triangles are similar, by AA Similarity Postulate, this formula works for all 45-45-90 triangles.

  3. Does it work for the Pythagorean Theorem? x ? x o 2x = 2x ? 2 2 45 o 45 Yes!

  4. The Two Types of 45-45-90 Problems Type 1: Given the length of a leg, solve for the other leg and hypotenuse. 3 What are the other two lengths? 3 o 45 o 45 o 45 Multiply by root 2. Multiply by root 2. o 45 What are the other two lengths?

  5. The Two Types of 45-45-90 Problems Type 2: Given the length of the hypotenuse, solve for the two legs. What are the other two lengths? Shortcut: o Divide the length of the hypotenuse by 2 and multiply by to find the length of the leg. 45 Divide by root 2. 7 o 45 Divide by root 2. o 45 o 45 What are the other two lengths?

  6. On your Notes complete:8.4 Day I: Part I and Part III (#1-2)8.4 Day 2: Part III

  7. HW • 8.4 Notes Day 1 Parts I and III (#1-2) 8.4 Notes Day 2 Part III P. 302 #1-8, 17, 18, 23, 26, 27

  8. 30-60-90 Triangles The formula. o 30 2x o 60 x Since all 30-60-90 triangles are similar, by AA Similarity Postulate, this formula works for all 30-60-90 triangles.

  9. Does it work for the Pythagorean Theorem? x ? x + 3x = 4x ? 2 2 2 o 60 Yes! 2x o 30

  10. The Three Types of 30-60-90 Problems Type 1: Given the length of the short leg, solve for the long leg and hypotenuse. 5 Multiply by root 3. o 60 Multiply by 2. o 30 10 o 30 What are the other two lengths? Multiply by root 3. Multiply by 2. o 60 What are the other two lengths?

  11. The Three Types of 30-60-90 Problems Type 2: Given the length of the hypotenuse, solve for the two legs. What are the other two lengths? Multiply by root 3. o 60 Divide by 2. o 60 9 o 30 Multiply by root 3. o 30 Divide by 2. What are the other two lengths?

  12. The Three Types of 30-60-90 Problems Type 3: Given the length of the long leg, solve for the short leg and hypotenuse. Divide by root 3. Shortcut: 9 o 60 Divide the length of the long leg by 3 and multiply by to find the length of the short leg. Multiply by 2 o 30 o 30 What are the other two lengths? Divide by root 3. o 60 Multiply by 2. What are the other two lengths?

  13. On your Notes complete:8.4 Day I: Part II and Part III (#3)8.4 Day 2: Part IV

  14. HW • 8.4 Packet Day 1 Parts II, III (#3) 8.4 Packet Day 2 Part IV pg. 301 #1-9 pg. 302 #21-25

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