9.3 Warmup Find the value of x and y
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1 9.3 Wrmup Find te vlue of x nd y x x Are tese te sides of tringle? If yes, is te cute, otuse or rigt?. 4, 4, 10 Mrc 3, 2017 y Geometry 9.1 Similr Rigt Tringles. 9, 15,12 c. 2, 3, 4 1
2 Geometry 9.3 Similr Rigt Tringles 9.3 Work Seet
3 9.3 Essentil Question How re ltitudes nd geometric mens of rigt tringles relted? Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 3
4 Gols Know proportions in similr rigt tringles. Solve prolems involving similr rigt tringles formed y ltitudes on te ypotenuse. Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 4
5 Mens (Averges) Aritmetic men of x & y: x y 2 Geometric men of x & y: xy Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 5
6 Geometric Men Te geometric men of two positive numers nd is te positive numer x tt stisfies x = x. So, x 2 = nd x =. Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 6
7 Exmple 1. Find te geometric men of 24 nd 48.. Find te geometric men of 18 nd 54. Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 7
8 Your Turn. Find te geometric men of 12 nd 27.. Find te geometric men of 16 nd 18. Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 8
9 Rememer AA~ for Tringles Teorem: If two ngles of one tringle re congruent to two ngles of noter tringle, ten te tringles re similr. (AA~ Postulte) Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 9
10 Rigt Tringle Similrity Teorem Strt wit rigt ABC wit ltitude CD (CD AB t D). C A D B Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 10
11 Rigt Tringle Similrity Teorem C A D B Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 11
12 Rigt Tringle Similrity Teorem C A D B Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 12
13 Rigt Tringle Similrity Teorem If te ltitude is drwn to te ypotenuse of rigt tringle, ten te two tringles formed re similr to te originl tringle nd to ec oter. C C C D B A A D B Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 13
14 Rigt Tringle Similrity Teorem ABC ~ ACD ~ CBD (AA~ Postulte) C C C D B A A D B Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 14
15 Rigt Tringle Similrity Teorem ABC ~ ACD ~ CBD For clrity, we nme te segments. C A y c D x B Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 15
16 ABC ~ ACD ~ CBD = y = x 2 = xy C = xy C C D x B A y D A Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 16 c B
17 ABC ~ ACD ~ CBD c = = x C 2 = xc = xc C C D x B A y D A Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 17 c B
18 ABC ~ ACD ~ CBD c = y = 2 = yc C = yc C C D x B A y D A Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 18 c B
19 ABC ~ ACD ~ CBD Similr Tringles Tese expressions re clled geometric mens. = xy C = xc = yc Mrc 3, 2017 A y c Geometry 9.3 Similr Rigt Tringles D x B 19
20 Teorem 9.7 Geometric Men (Altitude) Tm Te ltitude drwn to te ypotenuse of rigt tringle is te geometric men of te segments on te ypotenuse. = xy y x Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 20
21 Exmple 2 Find. = mn xy Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 21
22 Your Turn Find x. = mn xy 4 8x 16 8x x x Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 22
23 Teorem 9.8 Geometric Men (Leg) Tm Te lengt of ec leg of rigt tringle is te geometric men of te ypotenuse nd te segment of te ypotenuse djcent to tt leg. = xc = yc y c x Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 23
24 Exmple 3 Find &. 155 = xc = yc Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 24
25 Your Turn Find &. 102 = xc = yc Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 25
26 All you need to know ABC ~ ACD ~ CBD = xy = xc y c D x = yc Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 26
27 Quickly Complete te Eqution t 64 x 6 x 6 10 t 4 y = 4 10 y Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 27
28 Quickly Complete te Eqution y 4 11 x 7 x = 7 11 t 4 t = 7 4 y Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 28
29 Exmple 4: Solve for,, & c. 6 x c 4 Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 29
30 Solution 6 6 4x x c x x 9 Begin ere Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 30
31 Solution c Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 31
32 Solution Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 32
33 Solution Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 33
34 Tis is rd! No, it isn t. Ask: wt segment do you wnt to find? Wic oters do you need to know? Wic formul form? Solve te formul for te missing segment. Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 34
35 All you need to know ABC ~ ACD ~ CBD = xy = xc = yc y c D x Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 35
36 You do it. 615 Solve for,, Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 36
37 Try tis. Solve for d, e, & f. d 6 e f 6 = 4.5 f 36 = 4.5 f f = Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 37
38 Try tis. Solve for d, e, & f. d 6 e 8 d = 12.5(8) d = 100 d = e = 12.5(4.5) d = d = 7.5 Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 38
39 Is tis possile? No: Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 39
40 Homework Mrc 3, 2017 Geometry 9.3 Similr Rigt Tringles 40
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