1 / 58

Bellwork

Bellwork. Write everything you know about triangles. The. Pythagorean. Theorem. c. a. b. This is a right triangle:. We call it a right triangle because it contains a right angle. The measure of a right angle is 90 o. 90 o. in the. The little square.

darrion-carry
Download Presentation

Bellwork

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. Bellwork Write everything you know about triangles.

  2. The Pythagorean Theorem c a b

  3. This is a right triangle:

  4. We call it a right triangle because it contains a right angle.

  5. The measure of a right angle is 90o 90o

  6. in the The little square angle tells you it is a right angle. 90o

  7. About 2,500 years ago, a Greek mathematician named Pythagoras discovered a special relationship between the sides of right triangles.

  8. 5 3 4 Pythagoras realized that if you have a right triangle,

  9. 5 3 4 and you square the lengths of the two sides that make up the right angle,

  10. 5 3 4 and add them together,

  11. 5 3 4 you get the same number you would get by squaring the other side.

  12. Is that correct? ? ?

  13. 10 8 6 It is. And it is true for any right triangle.

  14. The two sides which come together in a right angle are called

  15. The two sides which come together in a right angle are called

  16. The two sides which come together in a right angle are called legs.

  17. The lengths of the legs are usually called a and b. a b

  18. The side across from the right angle is called the hypotenuse. a b

  19. And the length of the hypotenuse is usually labeled c. c a b

  20. The relationship Pythagoras discovered is now called The Pythagorean Theorem: c a b

  21. The Pythagorean Theorem says, given the right triangle with legs a and b and hypotenuse c, c a b

  22. then c a b

  23. You can use The Pythagorean Theorem to solve many kinds of problems. Suppose you drive directly west for 48 miles, 48

  24. Then turn south and drive for 36 miles. 48 36

  25. How far are you from where you started? 48 36 ?

  26. Using The Pythagorean Theorem, 48 482 + 362 = c2 36 c

  27. 48 482 + 362 = c2 36 c Why? Can you see that we have a right triangle?

  28. 48 482 + 362 = c2 36 c Which side is the hypotenuse? Which sides are the legs?

  29. Then all we need to do is calculate:

  30. So, since c2 is 3600, c is 60. And you end up 60 miles from where you started. So, since c2 is 3600, c is 48 36 60

  31. 15" 8" Find the length of a diagonal of the rectangle: ?

  32. 15" 8" Find the length of a diagonal of the rectangle: ? c b = 8 a = 15

  33. c b = 8 a = 15

  34. 15" 8" Find the length of a diagonal of the rectangle: 17

  35. Practice using The Pythagorean Theorem to solve these right triangles:

  36. c 5 12 = 13

  37. b 10 26

  38. b 10 26 = 24 (a) (c)

  39. 12 b 15 = 9

  40. Unit 3 Prior Vocabulary Gallery

  41. Adjacent Angles Angles in the same plane that have a common vertex and a common side, but no common interior points. In the figure above, angle FKI and angle FKH are adjacent angles.

  42. Transversal A line that crosses two or more lines.

  43. Alternate Interior Angles Pairs of angles formed when a third line (transversal) crosses two other lines and are on opposite sides of the transversal and are in between the other two lines. Angles 1,2,3, and 4 are interior angles. Angles 1 and 4 are alternate interior angles. Angles 2 and 3 are also alternate interior angles. Line t (in red) is called a transversal, a line crossing two or more lines.

  44. Same-Side Interior Angles Pairs of angles formed when a transversal (a third line) crosses two other lines. These angles are on the same side of the transversal and are outside the other two lines. Angles 1 and 3 are same-side interior angles and angles 2 and 4 are same-side interior angles.

  45. Alternate Exterior Angles: Pairs of angles formed when a transversal Crosses two other lines and are on opposite sides of the transversal and are Outside the other two lines. Angles 1, 2, 3, and 4 are all exterior angles. Angles 1 and 4 are alternate exterior angles. Angles 2 and 3 are also alternate exterior angles. Line t (in red) is called a transversal, a line Crossing two or more lines.

  46. Complementary Angles Two angles whose sum is 90º. In the example to the right, notice that at all times, angle BAT + angle CAT = 90º.The diagram to the left is the typical representation of complementary angle, but the angles do not have to be adjacent (as shown here) to be complementary.

  47. Congruent Having the same size, shape and measure. Notice that each figure below is congruent to one other figure in the given set of figures. The congruent pairs are congruent because they have the same size and shape, regardless of their orientation (the way they are "sitting").

  48. Corresponding Angles Angles that have the same relative positions in geometric figures. For example, in the figure below there are two triangles: a larger triangle, ABC, and a smaller triangle, ADE. Angles ADE and ABC are corresponding because they both lie in the same relative position in the two triangles. Angles ABC and AED are not corresponding since they do not lie in the same Relative position in the two triangles.

  49. Equiangular The property of a polygon whose angles are all congruent. For example, an equilateral triangle is equiangular since its interior angles are equal (to 60 degrees). In general, all regular polygons such as equilateral triangle, square, pentagon, and hexagon are equiangular.

  50. Equilateral The property of a polygon whose sides are all congruent.

More Related