1 / 33

8 th Grade Math

8 th Grade Math. 1 st Period Nov . 1, 2012. No HW Review; Start Warm-Up. Find the areas of the following: 1. 2. 3. 4. 5. . Warm-Up: Answers. Find the areas of the following: 1. 2. 3. 4. 5. What operation could be applied to the area in #5 to get the side length of the square?.

marvel
Download Presentation

8 th Grade Math

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 8th Grade Math 1st Period Nov. 1, 2012

  2. No HW Review; Start Warm-Up Find the areas of the following: 1. 2. 3. 4. 5.

  3. Warm-Up: Answers Find the areas of the following: 1. 2. 3. 4. 5. What operation could be applied to the area in #5 to get the side length of the square? A = 2 square units A = 1 square unit A = 4 square units A = 5 square units A = 1 square unit

  4. So, to find the diagonal distance between two points, you can … • Draw a line segment between the points. • Make a square with the segment as a side. • Find the area of the square. • Take the square root of the area.

  5. But … Do We Have to Make the Square Each Time?

  6. No! Notice that … = making + =

  7. If we remember our original line segment … is the hypotenuse of and we call the side lengths a, b, and c … a2 c b a + = b2 c2

  8. That is, we can find … the square of the hypotenuse by adding the squares of the legs c2 b2 a2 This fact is known as the Pythagorean Theorem!

  9. Looking for length of the hypotenuse a2 + b2 = c2 152 + 202 = x2 225 + 400 = x2 625 = x2 25 = x Using the Pythagorean Theorem x 15 20

  10. Looking for length of a leg a2 + b2 = c2 62 + x2 = 102 36 + x2 = 100 -36-36 x2 = 64 x = 8 Using the Pythagorean Theorem 10 6 x

  11. Looking for the diagonal distance a2 + b2 = c2 32 + 42 = x2 9 + 16 = x2 25 = x2 5 = x Using the Pythagorean Theorem x 3 4

  12. HW (Front & Back of the Same WS) • Applications #1-2, 5-6 (circled) • Using the Pythagorean Theorem in Word Problems #1 (circled)

  13. 8th Grade Math 2nd Period Nov. 1, 2012

  14. No HW Review; Start Warm-Up Find the areas of the following: 1. 2. 3. 4. 5.

  15. Warm-Up: Answers Find the areas of the following: 1. 2. 3. 4. 5. What operation could be applied to the area in #5 to get the side length of the square? A = 2 square units A = 1 square unit A = 4 square units A = 5 square units A = 1 square unit

  16. So, to find the diagonal distance between two points, you can … • Draw a line segment between the points. • Make a square with the segment as a side. • Find the area of the square. • Take the square root of the area.

  17. But … Do We Have to Make the Square Each Time?

  18. No! Notice that … = making + =

  19. If we remember our original line segment … is the hypotenuse of and we call the side lengths a, b, and c … a2 c b a + = b2 c2

  20. That is, we can find … the square of the hypotenuse by adding the squares of the legs c2 b2 a2 This fact is known as the Pythagorean Theorem!

  21. Looking for length of the hypotenuse a2 + b2 = c2 152 + 202 = x2 225 + 400 = x2 625 = x2 25 = x Using the Pythagorean Theorem x 15 20

  22. HW (Front & Back of the Same WS) • Applications #1-2, 5-6 (circled) • Using the Pythagorean Theorem in Word Problems #1 (circled)

  23. 8th Grade Math 4th Period Nov. 1, 2012

  24. No HW Review; Start Warm-Up Find the areas of the following: 1. 2. 3. 4. 5.

  25. Warm-Up: Answers Find the areas of the following: 1. 2. 3. 4. 5. What operation could be applied to the area in #5 to get the side length of the square? A = 2 square units A = 1 square unit A = 4 square units A = 5 square units A = 1 square unit

  26. So, to find the diagonal distance between two points, you can … • Draw a line segment between the points. • Make a square with the segment as a side. • Find the area of the square. • Take the square root of the area.

  27. But … Do We Have to Make the Square Each Time?

  28. No! Notice that … = making + =

  29. If we remember our original line segment … is the hypotenuse of and we call the side lengths a, b, and c … a2 c b a + = b2 c2

  30. That is, we can find … the square of the hypotenuse by adding the squares of the legs c2 b2 a2 This fact is known as the Pythagorean Theorem!

  31. Looking for length of the hypotenuse a2 + b2 = c2 152 + 202 = x2 225 + 400 = x2 625 = x2 25 = x Using the Pythagorean Theorem x 15 20

  32. Looking for the diagonal distance a2 + b2 = c2 32 + 42 = x2 9 + 16 = x2 25 = x2 5 = x Using the Pythagorean Theorem x 3 4

  33. HW (Front & Back of the Same WS) • Applications #1-2, 5-6 (circled) • Using the Pythagorean Theorem in Word Problems #1 (circled)

More Related