9.2 Dy 1 Wrm Up Find the vlue of. Give nswers s simplified rdicls. 1. 2. 3 3 3. 4. 10 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 1
Geometry 9.2 Specil Right Tringles
9.2 Essentil Question Wht is the reltionship mong the side lengths of 45-45 - 90 tringles? 30-60 - 90 tringles? Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 3
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
First, rdicl review: A rdicl in simplest form hs no perfect squres in the rdicnd. 20 4 5 4 5 2 5 150 25 6 25 6 5 6 45 9 5 3 5 Mrch 2, 2017 Geometry 9.4 Specil Right Tringles 5
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
Emples 10 10 2 10 2 2 2 2 2 24 24 3 24 3 3 3 3 3 5 2 8 3 9 9 2 9 2 2 2 2 2 4.5 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 7
Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 8
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
Constructing Specil Tringles Clen it up keep only the tringle on the right. Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 10
Constructing Specil Tringles In the originl squre, ech side ws the sme. Lbel them. Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 11
Constructing Specil Tringles Solve for the hypotenuse, c. 2 2 2 c c 2 2 2 2 c c 2 2 c 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 12
45-45-90 Tringle 45-45-90 Tringle Theorem (Thm 9.4) In 45-45 - 90 tringle, the hypotenuse is 2 times s long s ech leg. 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 13
Emple 1 Solve for & y. 2 5 2 y 5 5 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 14
Emple 2 Solve for & y. 2 8 2 8 y 8 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 15
Emple 3: A tougher one. Solve for & y. 2 10 y Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 16
Emple 3 Solution 10 5 2 y 5 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 17
45-45-90 Tringle Lern the pttern! 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 18
Try it. Find nd y. 8 y 4 2 4 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 19
45-45-90 Tringle Shortcut pttern: 2 2 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 20
Emple 4 Solve for & y 2 2 2 2 2 1600 2 40 800 800 400 2 20 2 40 20 2 20 2 y Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 21
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
Emple 5 Solution 30 2 30 ft. 30 2 42.43 ft. 42 ft 5 in. 30 ft. Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 23
9.2 Dy 2 Wrm Up Solve for the vrible. 1. 2. 12 3. 4. 8 X 4 3 4 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 24
Constructing Specil Tringles Construct n equilterl tringle. Ech ngle mesures. Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 25
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 30-60 - 90. 30 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 26
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
Constructing Specil Tringles This is clled 30 60 90 tringle. 30 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 28
Constructing Specil Tringles Give the originl side n rbitrry length. Cll it 2. 2 30 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 29
Constructing Specil Tringles Wht is the length of the bse? 2 30 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 30?
Constructing Specil Tringles Now find the height of the tringle, h. 2 + h 2 = (2) 2 2 30 h Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 31
Constructing Specil Tringles 2 2 2 h (2 ) 2 2 2 h 4 h 2 2 3 2 30 h 3 h h 3 3 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 32
30-60-90 Tringle 30-60-90 Tringle Theorem (Theorem 9.5) In 30-60 - 90 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
30-60-90 Tringle 3 30 2 3 2 3 3 30 30 3 2 3 2 3 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 34
Emple 6 Find & y. 30 2 30 3 12 y 6 3 Mrch 2, 2017 6 35 Geometry 9.2 Specil Right Tringles
Emple 7 Find & y. 30 2 30 3 16 8 3 y 8 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 36
Emple 8 Find & y. 30 2 30 3 y 40 20 3 20 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 37
Emple 9 Find & y. 30 y 12 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 38
Emple 9 Solution 30 y 12 8 3 4 3 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 39
30-60-90 Tringle Lern the pttern! 30 2 3 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 40
Try it. Find nd y. 30 30 y15 3 15 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 41
Another one: Find h nd y. 30 14 h7 3 y7 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 42
Agin: Find nd y. 30 4 2 3 y2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 43
Summry 30 2 2 3 45-45-90 30-60-90 In Trigonometry, you will understnd why these tringle re so importnt. Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 44
Quick Quiz 5 problems 1. Find & y. 30 12 3 y 24 12 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 45
2. Find & y. y 7 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 46
3. Find & y. 50 25 y 25 3 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 47
4. Find & y. 2 62 62 62 2 2 2 y 62 2 2 31 2 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 48
5. Find & y. y 3 75 75 3 3 3 75 25 3 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 49
6. Find & y. 9 3 y Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 50
One More Time 30 2 2 3 Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 51
Homework Mrch 2, 2017 Geometry 9.2 Specil Right Tringles 52