1. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles

2. What if we had an isosceles right triangle?

3. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles What if we had an isosceles right triangle? Do we know the measure of every angle?

4. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles What if we had an isosceles right triangle? Do we know the measure of every angle? The right angle is 90 degrees.

5. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles What if we had an isosceles right triangle? Do we know the measure of every angle? The right angle is 90 degrees. How much is left over? 180 – 90 = 90.

6. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles What if we had an isosceles right triangle? Do we know the measure of every angle? The right angle is 90 degrees. How much is left over? 180 – 90 = 90. But the other two angles are equal to each other.

7. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles What if we had an isosceles right triangle? Do we know the measure of every angle? The right angle is 90 degrees. How much is left over? 180 – 90 = 90. But the other two angles are equal to each other. 90 divided by 2 is 45. The other angles are 45 degrees each.

8. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles What if we had an isosceles right triangle? Do we know the measure of every angle? The right angle is 90 degrees. How much is left over? 180 – 90 = 90. But the other two angles are equal to each other. 90 divided by 2 is 45. The other angles are 45 degrees each.

9. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles We call this a 45, 45, 90 triangle.

10. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles We call this a 45, 45, 90 triangle. What if one leg had length x?

11. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles We call this a 45, 45, 90 triangle. What if one leg had length x? Note: the triangle has three sides. The longest side, across from the right angle, is called the hypotenuse. The other two sides are called legs.

12. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles We call this a 45, 45, 90 triangle. What if one leg had length x? Note: the triangle has three sides. The longest side, across from the right angle, is called the hypotenuse. The other two sides are called legs.

13. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles We call this a 45, 45, 90 triangle. What if one leg had length x?

14. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles We call this a 45, 45, 90 triangle. What if one leg had length x? How long is the other leg?

15. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles We call this a 45, 45, 90 triangle. What if one leg had length x? How long is the other leg?

16. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles We call this a 45, 45, 90 triangle. What if one leg had length x? How long is the other leg?

17. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles We call this a 45, 45, 90 triangle. What if one leg had length x? How long is the other leg? If both legs have length x, what is the length of the hypotenuse?

18. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles We call this a 45, 45, 90 triangle. What if one leg had length x? How long is the other leg? If both legs have length x, what is the length of the hypotenuse?

19. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles

27. This special triangle needs to be memorized.

28. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles This special triangle needs to be memorized. We now need to meet one more special right triangle.

29. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles This special triangle needs to be memorized. We now need to meet one more special right triangle.

30. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles We start with an equilateral triangle.

31. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles We start with an equilateral triangle. Since all three angles are the same, 180 divided by 3 is 60.

32. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles We start with an equilateral triangle. Since all three angles are the same, 180 divided by 3 is 60. All three sides are the same length. For fun, they will each be 2x.

33. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles We start with an equilateral triangle. Since all three angles are the same, 180 divided by 3 is 60. All three sides are the same length. For fun, they will each be 2x. Actually, it makes the math easier.

34. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles We start with an equilateral triangle. Since all three angles are the same, 180 divided by 3 is 60. All three sides are the same length. For fun, they will each be 2x. Actually, it makes the math easier. Now, cut the triangle in half.

35. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles

36. Now, toss away the old triangle.

37. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles Keep half of the new triangle.

38. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles

40. Obviously, 30 is half of 60.

41. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles Obviously, 30 is half of 60. Of course, x is half of 2x.

42. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles Obviously, 30 is half of 60. Of course, x is half of 2x. Now you see why I wanted to start with 2x.

43. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles Obviously, 30 is half of 60. Of course, x is half of 2x. Now you see why I wanted to start with 2x. What is the length of the third side?

44. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles

54. Memorize this triangle.

55. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles Memorize this triangle.

56. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles Find x and y.

57. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles Find x and y.

58. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles Find x and y.

59. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles Find x and y.

60. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles Find x and y.

61. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles Find x and y.

62. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles Find x and y. Let’s work on today’s assignment.

63. Geometry Day 9 Tuesday March 1 / Wednesday March 2 Special Right Triangles Find x and y. Let’s work on today’s assignment.