1. Success Criteria:  I can identify the pattern of special right triangles  I can put answers in standard radical form to identify patterns Today’s Agenda Do Now HW #23 Due Wednesday Discovery Activity Do Now: Find the value of the missing length. Put answer in simplest radical form. Discover the side length patterns of special right triangles

2. Materials Needed: Equilateral Triangle (cut out) Ruler (cut out) – share with group Calculator Worksheet: Math 2 Task Notes Notebook

3. Discover the side length patterns of special right triangles Materials Needed: Equilateral Triangle (cut out) Ruler (cut out) – share with group Calculator Worksheet: Math 2 Task Notes Notebook

4. Discover the side length patterns of special right triangles

8. 6. Describe the pattern you see: What do you see?

9. Discover the side length patterns of special right triangles

11. Success Criteria:  I can identify the pattern of special right triangles  I can apply patterns of special right triangles to solve triangles. Today’s Agenda Do Now Discovery Activity HW #27 Due Wednesday Do Now: Rhombuses and Rectangles are parallelograms with special properties. List the special properties of each. I can discover the side length patterns of special right triangles, and apply them to solve triangles.

12. Discover the side length patterns of special right triangles All of the properties of a rectangle All of the properties of a rhombus Using the properties above label the angles of the square.

13. Discover the side length patterns of special right triangles 13 Label all the side lengths of your square. 13

14. Discover the side length patterns of special right triangles 45-45-90 The diagonals of a square _________ the angles. 13

15. Use the Pythagorean theorem to find the length of your diagonal. Discover the side length patterns of special right triangles

16. Now try another problem. It may help you to draw out the square with the diagonal in order to see the triangles. Discover the side length patterns of special right triangles

17. Now try a similar problem with a softball diamond. It may help to draw the square out. Discover the side length patterns of special right triangles 5

18. What did you learn about special right triangles? (Specifically 45-45-90 Triangles) Discover the side length patterns of special right triangles

19. Homework # 27 Pg.504 23-28 Discover the side length patterns of special right triangles

20. Success Criteria:  I can use the ratios of the 2 special cases of right triangles to solve problems  I can recognize the difference between the special right triangles Today’s Agenda Do Now Do Now: 8.2 Special Right Triangles Understanding the 2 special cases of the ratios of sides of right triangles Find the values of the variables. Give your answers in simplest radical form. 1. 2. x = 10; y = 20

22. Example 1: Finding Side Lengths in a 45 ° - 45º- 90º Triangle Find the value of x. Give your answer in simplest radical form. By the Triangle Sum Theorem, the measure of the third angle in the triangle is 45°. So it is a 45°-45°- 90° triangle with a leg length of 8.

23. Example 2: Finding Side Lengths in a 45º- 45º- 90º Triangle Find the value of x. Give your answer in simplest radical form. The triangle is an isosceles right triangle, which is a 45°-45°-90° triangle. The length of the hypotenuse is 5.

24. Example 3 Find the value of x. Give your answer in simplest radical form. x = 20 Simplify. By the Triangle Sum Theorem, the measure of the third angle in the triangle is 45°. So it is a 45°-45°- 90° triangle with a leg length of

25. Example 4 Find the value of x. Give your answer in simplest radical form. The triangle is an isosceles right triangle, which is a 45°-45°-90° triangle. The length of the hypotenuse is 16.

26. A 30°-60°-90° triangle is another special right triangle. You can use an equilateral triangle to find a relationship between its side lengths.

27. Example 5: Finding Side Lengths in a 30º-60º-90º Triangle Find the values of x and y. Give your answers in simplest radical form. Hypotenuse = 2(shorter leg)22 = 2x Divide both sides by 2.11 = x Substitute 11 for x.

28. Example 6 Find the values of x and y. Give your answers in simplest radical form. Hypotenuse = 2(shorter leg) Divide both sides by 2. y = 27Substitute for x.

29. Example 7 Find the values of x and y. Give your answers in simplest radical form. Simplify. y = 2(5) y = 10

30. Example 8 Find the values of x and y. Give your answers in simplest radical form. Hypotenuse = 2(shorter leg) Divide both sides by 2. Substitute 12 for x. 24 = 2x 12 = x

31. Example 9 Find the values of x and y. Give your answers in simplest radical form. Hypotenuse = 2(shorter leg) x = 2y Simplify. Substitute

32. Assignment #28 Posted to my website – complete in your notebook

33. Do Now Find the values of the variables. Give your answers in simplest radical form. 1. 2. x = 10; y = 20

34. Lesson Quiz: Part I Find the values of the variables. Give your answers in simplest radical form. 1. 2. 3. 4. x = 10; y = 20

35. Lesson Quiz: Part II Find the perimeter and area of each figure. Give your answers in simplest radical form. 5. a square with diagonal length 20 cm 6. an equilateral triangle with height 24 in.

36. Do Now: Finding Side Lengths in a 30º-60º-90º Triangle Find the values of x and y. Give your answers in simplest radical form. Hypotenuse = 2(shorter leg)22 = 2x Divide both sides by 2.11 = x Substitute 11 for x.