Pre-AP Geometry Worksheet 5.2: Similar Right Triangles

Transcription

1 ! re-a Geometr Worksheet 5.2: Similr Right Tringles Nme: te: eriod: Solve. Show ll work. Leve nswers s simplified rdicls on #1-5. For #6, round to the nerer tenth. 12!! 6! 1) =! 8! 6! 2) = 18! 8! w!+!9! 3) w = re-a Geometr Worksheet 5.2

2 !! 15! w!! 9! 4) w = ; = ; = c! 4! d! 8!! 5) = ; c = ; d = 6) You live on the corner of l Avenue nd Min Street. You drive from our prtment due south 9.9 miles on Min Street, then due west 13.2 miles on Stte Street to the corner of l Avenue nd Route 35. You turn left, hed for store t the intersection of Route 35 nd Min Street, then tke Min Street home from the store. l Avenue nd Route 35 re stright nd perpendiculr to ech other. ) Wht is the totl distnce ou trvel? (Round to the nerer tenth of mile.) b) Oklnd Street is prllel to Stte Street nd psses through the intersection where ou live. Your friend lives t the intersection of Oklnd nd Route 35. How fr prt do ou nd our friend live? (Round to the nerer tenth of mile.) re-a Geometr Worksheet 5.2

3 ONLI NE H O M E W O R K RATIE nd ALIATION EXERISES Scn pge for Virtul Nerd tutoril video. Write similrit sttement relting the three tringles in ech digrm. For dditionl support when completing our homework, go to ersontexas.com. 1. L N Q M J S K R O N Find the geometric men of ech pir of numbers nd nd nd 125 Select Techniques to Solve roblems (1)() Solve for nd STEM 11. Anlze Mthemticl Reltionships (1)(F) The rchitect s side view drwing of sltbo-stle house shows post tht supports the roof ridge. The support post is 10 ft tll. How fr from the front of the house is the support post positioned? 12.. The ltitude to the hpotenuse of right tringle divides the hpotenuse into segments 2 cm nd 8 cm long. Find the length of the ltitude to the hpotenuse. b. Use ruler to mke n ccurte drwing of the right tringle in prt (). c. escribe how ou drew the tringle in prt (b). Find the geometric men of ech pir of numbers nd nd nd nd nd 17 Front edroom Living room 25 ft Support post Kitchen ck 18. Evlute Resonbleness (1)() A clssmte ss the following sttement is true: The geometric men of positive numbers nd b is 1b. o ou gree? Eplin. 19. Write ll possible similrit sttements relting pirs of tringles in the digrm t the right. 20. Use roblem-solving Model (1)() The ltitude to the hpotenuse of right tringle divides the hpotenuse into segments with lengths in the rtio 1 : 2. The length of the ltitude is 8. How long is the hpotenuse? Q T S R ersontexas.com 403

4 Use the digrm for Eercises 21 nd Write prgrph proof of Theorem 9-3. Given: Right E with right E nd ltitude F rove: FE E, F E, FE F 22. Write two-column proof to prove tht F F = F EF. Given: Right E with right E nd ltitude F rove: F F = F EF E F For Eercises 23 nd 24, WXY is right tringle with ltitude YZ. 23. Which segment s length is geometric men bsed on orollr 1 to Theorem 9-3? Set up proportion bsed on the corollr. 24. Which two segments lengths re geometric mens bsed on orollr 2 to Theorem 9-3? Set up two proportions bsed on the corollr. W Y Z X 25. Evlute Resonbleness (1)() roblem 1 used the AA Similrit ostulte to prove Theorem 9-3. A clssmte ss tht it is just s es to use the SAS Similrit ostulte becuse if tringles re similr, then ll pirs of corresponding sides re proportionl. o ou gree with our clssmte? Eplin. Find the vlue of Use the figure t the right for Eercises 30 nd rove orollr 1 to Theorem rove orollr 2 to Theorem 9-3. Given: Right A with ltitude Given: Right A with ltitude to the hpotenuse to the hpotenuse rove: A = rove: A A = A A, A = A 32. Given: Right A with ltitude to the hpotenuse A rove: The product of the slopes of perpendiculr lines is onsider the following conjecture: The product of the lengths of the two legs of right tringle is equl to the product of the lengths of the hpotenuse nd the ltitude to the hpotenuse. rw figure for the conjecture. Write the Given informtion nd wht ou re to rove. A O b c b. Eplin Mthemticl Ides (1)(G) Is the conjecture true? Eplin. 404 Lesson 9-4 Similrit in Right Tringles

5 34. Appl Mthemtics (1)(A) To estimte the height of stone figure, An holds smll squre up to her ees nd wlks bckwrd from the figure. She stops when the bottom of the figure ligns with the bottom edge of the squre nd the top of the figure ligns with the top edge of the squre. Her ee level is 1.84 m from the ground. She is 3.50 m from the figure. Wht is the height of the figure to the nerest hundredth of meter? 35. Anlze Mthemticl Reltionships (1)(F) is the ltitude to the hpotenuse of right A. The coordintes of A,, nd re (4, 2), (4, 6), nd (4, 15), respectivel. Find ll possible coordintes of point m The digrm shows the prts of right tringle with n ltitude to the hpotenuse. For the two given mesures, find the other four. Use simplest rdicl form m 36. h = 2, s 1 = = 6, s 1 = / 1 = 2, s 2 = s 1 = 3, / 2 = 613 h s 1 s In the digrm, c = +. Use orollr 2 to Theorem 9-3 to write two more equtions involving, b, c,, nd. b. The equtions in prt () form sstem of three equtions in five vribles. Reduce the sstem to one eqution in three vribles b eliminting nd. c. Stte in words wht the one resulting eqution tells ou. 41. Given: In right A, # A, nd E #. rove: A = E E A E c b TEXAS Test rctice 42. The ltitude to the hpotenuse of right tringle divides the hpotenuse into segments of lengths 5 nd 15. Wht is the length of the ltitude? A A tringle hs side lengths 3 in., 4 in., nd 6 in. The longest side of similr tringle is 15 in. Wht is the length of the shortest side of the similr tringle? F. 1 in. G. 1.2 in. H. 7.5 in. J. 10 in. 44. Two students disgree bout the mesures of ngles in kite. The know tht two ngles mesure 124 nd 38, but the get different nswers for the other two ngles. n the both be correct? Eplin. ersontexas.com 405