Find the value of x. Give answers as simplified radicals.

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1 9.2 Dy 1 Wrm Up Find the vlue of. Give nswers s simplified rdicls Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 1

2 Geometry 9.2 Specil Right Tringles

3 9.2 Essentil Question Wht is the reltionship mong the side lengths of tringles? tringles? Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 3

4 Gols Know the side lengths of specil right tringles. Use specil right tringles to solve problems. Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 4

5 First, rdicl review: A rdicl in simplest form hs no perfect squres in the rdicnd Mrch 2, 2017 Geometry 9.4 Specil Right Tringles 5

6 Rtionlizing Denomintors This mens no squre roots llowed in the denomintor of frctions. Generl rule is to multiply numertor nd denomintor by the rdicl nd simplify. n n n n n n Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 6

7 Emples Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 7

8 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 8

9 Constructing Specil Tringles Given Squre. Drw one digonl. The digonl bisects the ngles. 1 & 2 mesure. 1 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 9

10 Constructing Specil Tringles Clen it up keep only the tringle on the right. Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 10

11 Constructing Specil Tringles In the originl squre, ech side ws the sme. Lbel them. Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 11

12 Constructing Specil Tringles Solve for the hypotenuse, c c c c c 2 2 c 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 12

13 Tringle Tringle Theorem (Thm 9.4) In tringle, the hypotenuse is 2 times s long s ech leg. 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 13

14 Emple 1 Solve for & y y 5 5 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 14

15 Emple 2 Solve for & y y 8 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 15

16 Emple 3: A tougher one. Solve for & y y Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 16

17 Emple 3 Solution y 5 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 17

18 Tringle Lern the pttern! 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 18

19 Try it. Find nd y. 8 y Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 19

20 Tringle Shortcut pttern: Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 20

21 Emple 4 Solve for & y y Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 21

22 Emple 5 A designer wnts to put rope light on the digonl of squre dnce floor. If the floor mesures 30 ft. on side, how long does the rope light need to be? Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 22

23 Emple 5 Solution ft ft. 42 ft 5 in. 30 ft. Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 23

24 9.2 Dy 2 Wrm Up Solve for the vrible X Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 24

25 Constructing Specil Tringles Construct n equilterl tringle. Ech ngle mesures. Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 25

26 Constructing Specil Tringles Drw n ltitude. It is perpendiculr to the bse. It lso bisects the verte ngle. The ltitude divides the tringle into two congruent tringles with ngles mesures of Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 26

27 Constructing Specil Tringles Clen up the drwing only keep the tringle on the left. 30 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 27

28 Constructing Specil Tringles This is clled tringle. 30 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 28

29 Constructing Specil Tringles Give the originl side n rbitrry length. Cll it Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 29

30 Constructing Specil Tringles Wht is the length of the bse? Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 30?

31 Constructing Specil Tringles Now find the height of the tringle, h. 2 + h 2 = (2) h Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 31

32 Constructing Specil Tringles h (2 ) h 4 h h 3 h h Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 32

33 Tringle Tringle Theorem (Theorem 9.5) In tringle, the hypotenuse is twice s long s the shorter leg, nd the longer leg is 3 times s long s the shorter leg. Hypotenuse 2 30 Short leg 3 Long leg Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 33

34 Tringle Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 34

35 Emple 6 Find & y y 6 3 Mrch 2, Geometry 9.2 Specil Right Tringles

36 Emple 7 Find & y y 8 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 36

37 Emple 8 Find & y y Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 37

38 Emple 9 Find & y. 30 y 12 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 38

39 Emple 9 Solution 30 y Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 39

40 Tringle Lern the pttern! Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 40

41 Try it. Find nd y y Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 41

42 Another one: Find h nd y h7 3 y7 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 42

43 Agin: Find nd y y2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 43

44 Summry In Trigonometry, you will understnd why these tringle re so importnt. Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 44

45 Quick Quiz 5 problems 1. Find & y y Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 45

46 2. Find & y. y 7 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 46

47 3. Find & y y 25 3 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 47

48 4. Find & y y Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 48

49 5. Find & y. y Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 49

50 6. Find & y. 9 3 y Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 50

51 One More Time Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 51

52 Homework Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 52

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