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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. All you need to know is how to multiply by root two and divide by root two. 45-45-90 Triangles. The formula. o. 45. x. o. 45. x.

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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. All you need to know is how to multiply by root two and divide by root two.

  3. 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.

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

  5. 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?

  6. 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?

  7. A 45 leg 45 C B leg

  8. Let’s Try Some From the HW • P. 302 #18, 26 • P. 288 #28

  9. HW • P. 302 (1-8, 17, 18, 23, 26, 27) • P. 288 #27-30 • Quiz on Thursday • Please sign up for School Loops(there is a link on my webpage) • Answers to the packet below if you want to work them out:

  10. Geometry 8.4 Special Right Triangles Part 2 This is a very important section, as it is used extensively throughout the second semester.

  11. All you need to know is how to multiply and divide by two and multiply and divide by root three.

  12. 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.

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

  14. 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?

  15. 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?

  16. 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?

  17. A 30 2(leg) 60 B C leg

  18. 1. x 6 x 10 x 45 45 60 x x 9 III. Solve for x. x

  19. Let’s Try A Few From the HW • P. 302 #20, #22 P. 288 #31

  20. HW P. 302 (9-16) P. 302 (19-25, skip 23) P. 288 (31,32) Quiz Friday Here are the answers to your packet if you want to work them out.

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