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Geometry

Geometry. 8.2 The Pythagorean Theorem (This section, along with 8.4, are very important as they are utilized throughout the second semester). Radical Review. Simplify each expression. = 8/3. = 5. You try!. = 28. = 9/5. Do you know these?. 2. 2. 14 =. 196. 7 =. 49. 2. 8 =. 64.

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Geometry

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  1. Geometry 8.2 The Pythagorean Theorem (This section, along with 8.4, are very important as they are utilized throughout the second semester)

  2. Radical Review • Simplify each expression. = 8/3 = 5 You try! = 28 = 9/5

  3. Do you know these? 2 2 14 = 196 7 = 49 2 8 = 64 2 13 = 169 2 2 15 = 225 9 = 81 2 12 = 2 144 10 = 100 2 16 = 256 2 11 = 2 121 17 = 289

  4. Pythagorean Theorem • In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. A c b C a B

  5. Pythagorean Theorem Proof This is in the state standards and may be on the STAR test! It is important to get this down! c Area of large square = Area of large square c ½ ab a a large square = 4 triangles + small square b ½ ab (b – a) 2 2 2 4(½ ab) + (b – 2ab + a ) c = c (b – a) b c c 2 2 b – 2ab + a 2 2 b 2 c = 2ab + b – 2ab + a c (b – a) ½ ab (b – a) 2 2 2 c = b + a a 2 2 b 2 c a + b = ½ ab a c c (b – a)(b – a) 2 2 b – 2ab + a

  6. Find the value of x together. # BC AC AB x 1) 8 6 x = 10 B 15 2) x 9 x = 12 7) 12 x x = A C

  7. Find the value of x on your own. Try #3, 4 and 8. Who can solve these on the board? # BC AC AB x = x B 3) 5 5 4) x 3 x = 6 5) x 1 x = 1 2 6) 1 x x = A C 12 8) x 8 x =

  8. 6 x 3 Solve for x. 9) 2 2 2 3 + 6 = x 2 9 + 36 = x 6 2 45 = x 9 5 3 3

  9. 17 x 15 6 Solve for x. 16) y 2 2 2 15 + y = 17 2 225 + y = 289 2 y = 64 y = 8 2 2 2 6 + 8 = x You may recognize this one, x = 10.

  10. 18) The diagonals of a rhombus have lengths 18 and 24. Find the perimeter of the rhombus. A rhombus has perpendicular diagonals. 2 2 2 9 + 12 = x x 15 15 2 12 81 + 144 = x 2 225 = x 9 x = 15 15 15 Thus, the perimeter is 60. A rhombus is a parallelogram. Diagonals of a parallelogram bisect each other.

  11. Reminders • The diagonals of a rhombus are perpendicular to each other. • The altitude drawn to the base of an isosceles triangle is perpendicular to the base at its midpoint.

  12. HW • Complete #1-20 from the packet on a separate sheet. For any ones we have done already, write “Did in Class” • P. 292 #19-22 • P. 289 (32-38 Even)

  13. Part of the HW, Answers to exercises #10-20 Skip 14, 16, 18, 20. 10) x = 17 11) x = 4 12) x = 3 13) x = 8 14) 15) 17) 19) 20) x = 7

  14. Let’s review the triangle proportion formulas from 8.1 and do # on page

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