45 45-90 triangles

1. Special Right Triangles 45 – 45 – 90 Triangles

2. Special Right Triangles Directions As you view this presentation, take notes and work out the practice problems. When you get to the practice problem screens, complete the step in your notebook before continuing to the next slide.

3. 45- 45- 90 Triangles A 45 – 45 – 90 triangle is also known as an isosceles right triangle. An isosceles right triangle is a right triangle with 2 equal sides or legs. (a = b) The 2 angles across from the equal sides each measure 45 o . (angle A = angle B = 45 o ) c a b 45 o 45 o A C B

4. 45- 45- 90 Triangles Because the lengths of the 2 legs in 45 – 45 – 90 triangle are equal, the legs are usually labeled x. The hypotenuse in a 45-45-90 triangle is often labeled h. h x x 45 o 45 o

5. 45- 45- 90 Triangles Finding the Length of the Hypotenuse The Pythagorean Theorem can be used to find the length of the hypotenuse when given the length of the legs. x 2 + x 2 = h 2 2x 2 = h 2 = h 2 x = h You can save a lot of time and work if you remember h = x   h x x 45 o 45 o

6. 45- 45- 90 Triangles Practice Problem 1 Find the length of x h x = ? 5 45 o 45 o

7. 45- 45- 90 Triangles Practice Problem 1 Find the length of x The two legs of a 45 – 45 – 90 triangle are equal so x = 5 h x = 5 5 45 o 45 o

8. 45- 45- 90 Triangles Practice Problem 1 Find the length of h h = ? x= 5 5 45 o 45 o

9. 45- 45- 90 Triangles Practice Problem 1 Find the length of h You can always use the Pythagorean Theorem to find the length of h. But if you remember the shortcut h = x   x = 5 5 45 o 45 o

10. 45- 45- 90 Triangles Practice Problem 1 Find the length of h You can always use the Pythagorean Theorem to find the length of h. But if you remember the shortcut h = 5   h = 5   x = 5 5 45 o 45 o

11. 45- 45- 90 Triangles Finding the Lengths of the Legs The Pythagorean Theorem can be used to find the lengths of the legs when given the length of the hypotenuse. x 2 + x 2 = h 2 2x 2 = h 2 x 2 = = x = * = ( R emember to always rationalize the denominator)   h x x 45 o 45 o

12. 45- 45- 90 Triangles Finding the Lengths of the Legs You can save a lot of time and work if you remember x =   h x =   x =   45 o 45 o

13. 45- 45- 90 Triangles Practice Problem 2 Find the length of x h = 3 x = ? x = ? 45 o 45 o

14. 45- 45- 90 Triangles Practice Problem 2 Find the length of x You can always use the Pythagorean Theorem to find the lengths of the legs. h = 3 x =   x = ? 45 o 45 o

15. 45- 45- 90 Triangles Practice Problem 2 Find the length of x But if you remember the shortcut x =   h = 3 x =   45 o 45 o x =  

16. 45- 45- 90 Triangles Practice Problem 2 Find the length of x But if you remember the shortcut x = Then x =   h = 3 x =   45 o 45 o x =  

17. 45- 45- 90 Triangles Practice Problem 3 Find the length of x h = 1 x = ? x = ? 45 o 45 o

18. 45- 45- 90 Triangles Practice Problem 3 Find the length of x You can always use the Pythagorean Theorem to find the lengths of the legs. h = 1 x =   x = ? 45 o 45 o

19. 45- 45- 90 Triangles Practice Problem 3 Find the length of x But if you remember the shortcut x =   h = 1 x =   45 o 45 o x =  

20. 45- 45- 90 Triangles Practice Problem 3 Find the length of x But if you remember the shortcut x = Then x = =   h = 1 x =   45 o 45 o x =  

21. 45- 45- 90 Triangles in the Unit Circle In the Unit Circle: h = 1 So remembering this shortcut for a 45 – 45 - 90 triangle will save you time and work . x =   h = 1 x =   45 o 45 o x =