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. You try! = 5 = 8/3 = 28= 9/5

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

4. Pythagorean Theorem  In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. a b c 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! b c a a a a b b b c c c ½ ab (b – a) Area of large square = Area of large square c 2 = 4 triangles + small square c 2 = 4(½ ab) + (b – a)(b – a) b – 2ab + a 22 b – 2ab + a 22 large square = (b – 2ab + a ) 22 2ab +b – 2ab + a 22 c 2 =b + a 22 cc c c c 2 =a + b 22

6. Find the value of x together. C A B #BCACAB 1)86 x 2)x9 15 7)12x x = 10 x = 12 x =

7. Find the value of x on your own. C A B #BCACAB 3)55 x 4)x3 Try #3, 4 and 8. Who can solve these on the board? x = 6)1x 5)x1 x = 1 8)x8 x = 6 12 2

8. Solve for x. 3 6 x 9) 6 3 + 6 = x 222 9 + 36 = x 2 45 = x 2 9 5 3

9. Solve for x. 16) y 15 + y = 17 222 225 + y = 289 2 y = 64 2 15 17 6 x y = 8 6 + 8 = x 222 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. A rhombus is a parallelogram. Diagonals of a parallelogram bisect each other. 9 12 9 + 12 = x 222 x 81 + 144 = x 2 225 = x 2 x = 15 15 Thus, the perimeter is 60.

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