# Skills Practice Skills Practice for Lesson 4.1

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1 Skills Prctice Skills Prctice for Lesson.1 Nme Dte Tiling Bthroom Wll Simplifying Squre Root Expressions Vocbulry Mtch ech definition to its corresponding term. 1. n expression tht involves root. rdicnd 2. the symbol b. squre root of number 3. number b such tht b 2 c. simplest form. when the rdicnd of rdicl expression contins d. rdicl sign no fctors tht re perfect squres 5. n expression under rdicl sign e. perfect squre 6. n integer tht cn be written s the squre of some f. rdicl expression other integer Problem Set Clculte the vlue of ech rdicl expression Chpter Skills Prctice 107

2 Simplify ech expression nd write the result in rdicl form Nme the form of 1 tht you would use to simplify ech frction Simplify ech frction Chpter Skills Prctice

3 Nme Dte Given the re A of squre, clculte the length of one side. 35. A cm A 75 m 2 Chpter Skills Prctice 109

4 37. Ingrid covers the floor of squre room with 196 lrge tiles. The re of ech tile is 1 squre foot. Wht is the length of one side of the room? 3. Devon prepres squre grden with n re of 10 squre feet. How much fencing will Devon need for ech side of the grden? 110 Chpter Skills Prctice

5 Skills Prctice Skills Prctice for Lesson.2 Nme Dte Instlling Stellite Dish The Pythgoren Theorem Vocbulry Define ech term in your own words. 1. right tringle 2. legs 3. hypotenuse. Pythgoren Theorem 5. Converse of the Pythgoren Theorem Chpter Skills Prctice 111

6 Problem Set Determine the length of the hypotenuse of ech tringle. Round your nswer to the nerest tenth, if necessry c 6 c. 9. c 10 c Chpter Skills Prctice

7 Nme Dte Determine the length of the unknown leg. Round your nswer to the nerest tenth, if necessry b b 5 Chpter Skills Prctice 113

8 Use the converse of the Pythgoren Theorem to determine whether ech tringle is right tringle. Explin your nswer Chpter Skills Prctice

9 Nme Dte Use the Pythgoren Theorem to clculte ech unknown length. Round your nswer to the nerest tenth, if necessry. 1. Chndr hs ldder tht is 20 feet long. If the top of the ldder reches 16 feet up the side of building, how fr from the building is the bse of the ldder? 19. A scffold hs digonl support bem to strengthen it. If the scffold is 12 feet high nd 5 feet wide, how long must the support bem be? Chpter Skills Prctice 115

10 20. The length of the hypotenuse of right tringle is 0 centimeters. The legs of the tringle re the sme length. How long is ech leg of the tringle? 21. A crpenter props ldder ginst the wll of building. The bse of the ldder is 10 feet from the wll. The top of the ldder is 2 feet from the ground. How long is the ldder? 116 Chpter Skills Prctice

11 Skills Prctice Skills Prctice for Lesson.3 Nme Dte D rfting Equipment Properties of 5º-5º-90º Tringles Vocbulry Explin why ech term correctly describes the figure below isosceles right tringle 2. 5º-5º-90º tringle Problem Set Determine the length of the hypotenuse of ech 5º-5º-90º tringle. Write your nswer s rdicl in simplest form in. c 5 cm c 5. 9 ft 2 in. c 6. 7 km 5 cm c 9 ft 7 km Chpter Skills Prctice 117

12 Determine the lengths of the legs of ech 5º-5º-90º tringle. Write your nswer s rdicl in simplest form cm 12 mi ft 2 m Use the given informtion to nswer ech question. Round your nswer to the nerest tenth, if necessry. 11. Soren is flying kite on the bech. The string forms 5º ngle with the ground. If he hs let out 16 meters of line, how high bove Soren is the kite? 11 Chpter Skills Prctice

13 Nme Dte 12. Meen is picking ornges from the tree in her yrd. She rests 12-foot ldder ginst the tree t 5º ngle. How fr is the top of the ldder from the ground? 13. Emily is building squre bookshelf. She wnts to dd digonl support bem to the bck to strengthen it. The digonl divides the bookshelf into two 5º-5º-90º tringles. If ech side of the bookshelf is feet long, wht must the length of the support bem be? 1. Prospect Prk is squre with side lengths of 512 meters. One of the pths through the prk runs digonlly from the northest corner to the southwest corner, nd divides the prk into two 5º-5º-90º tringles. How long is tht pth? Determine whether the tringle is 5º-5º-90º tringle. Explin how you know Chpter Skills Prctice 119

14 Determine the re of ech tringle mm 120 Chpter Skills Prctice

15 Nme Dte in ft m Chpter Skills Prctice 121

16 Use the given informtion to nswer ech question. 23. Eli is mking mosic using tiles shped like 5º-5º-90º tringles. The length of the hypotenuse of ech tile is 13 centimeters. Wht is the re of ech tile? 2. Bked pit chips re often in the shpe of 5º-5º-90º tringles. Citlyn finds tht the longest side of pit chip in one bg mesures 3 centimeters. Wht is the re of the pit chip? 25. Annik is mking kite in the shpe of 5º-5º-90º tringle. The longest side of the kite is 2 inches. Wht is the re of the piece of fbric needed for the kite? 122 Chpter Skills Prctice

17 Nme Dte 26. A tent hs mesh door tht is shped like 5º-5º-90º tringle. The longest side of the door is 36 inches. Wht is the re of the mesh door? Chpter Skills Prctice 123

18 12 Chpter Skills Prctice

19 Skills Prctice Skills Prctice for Lesson. Nme Dte Finishing Concrete Properties of 30º-60º-90º Tringles Vocbulry Write the term tht best completes ech sttement. 1. A 30º- -90º tringle is formed by dividing n tringle in hlf by its ltitude. 2. The 30º-60º-90º Tringle Theorem sttes tht the length of the hypotenuse is times the length of the shorter leg, nd the length of the longer leg is the length of the shorter leg. times Problem Set Determine the mesure of the indicted interior ngle. 3. B A C. D 30 E G F m ABC m DFE 5. H R J A K S A T m HAK m TRA Given the length of the short leg of 30º-60º-90º tringle, determine the lengths of the long leg nd hypotenuse. Write your nswers s rdicls in simplest form ft 60 c b in. c b Chpter Skills Prctice 125

20 mm b c cm 60 c b 30 Given the length of the hypotenuse of 30º-60º-90º tringle, determine the lengths of the two legs. Write your nswers s rdicls in simplest form m km b 30 b yd b ft b 30 Given the length of the long side of 30º-60º-90º tringle, determine the lengths of the short leg nd hypotenuse. Write your nswers s rdicls in simplest form c 3 in c 11 3 m Chpter Skills Prctice

21 Nme Dte c c mi 30 1 ft c 60 c m 30 1 in. Determine the re of ech 30º-60º-90º tringle. Round your nswer to the nerest tenth, if necessry cm b 30 Chpter Skills Prctice 127

22 km b Universl Sporting Goods sells pennnts in the shpe of 30º-60º-90º tringles. The length of the longest side of ech pennnt is 16 inches. 2. A fctory produces solid drfting tringles in the shpe of 30º-60º-90º tringles. The length of the side opposite the right ngle is 15 centimeters. 12 Chpter Skills Prctice

23 Nme Dte Determine the volume of the right tringulr prism. Round your nswer to the nerest tenth, if necessry ft ft m 30 2 m Chpter Skills Prctice 129

24 27. Ingrid built len-to shelter while cmping in the wilderness. The len-to shelter hs the dimensions shown in the digrm, nd meets the ground t 30º ngle. Wht is the volume of the len-to shelter? 60 5 ft 30 6 ft 2. The roof of Joshu s house meets the front of the house t 60º ngle, forming n ttic in the shpe of 30º-60º-90º tringulr prism. The front of the house is 0 feet wide, nd the length of the roof is 50 feet long the incline, s shown in the digrm. Wht is the volume of the ttic? 50 ft 0 ft 130 Chpter Skills Prctice

25 Skills Prctice Skills Prctice for Lesson.5 Nme Dte Meeting Friends The Distnce Formul Vocbulry Define ech term in your own words. 1. coordinte plne 2. Distnce Formul Problem Set Archeologists mp the loction of ech item they find t dig on 1 foot 1 foot coordinte grid. Clculte the distnce between ech pir of objects on the given coordinte plne. Explin how you found your nswer. 3. Wht is the distnce between the spindle nd the pottery shrd? y spindle pottery shrd x Chpter Skills Prctice 131

26 . Wht is the distnce between the coins nd the spindle? y spindle coins x 5. Wht is the distnce between the beds nd the spindle? y spindle beds x 132 Chpter Skills Prctice

27 Nme Dte 6. Wht is the distnce between the coins nd the pottery shrd? y coins 3 2 pottery shrd x Clculte the distnce between ech pir of coordinte points. Round your nswer to the nerest tenth, if necessry. 7. (3, ) nd (9, 7) Chpter Skills Prctice 133

28 . (, 2) nd (6, ) 9. (1, 3) nd (9, ) 10. (3, 5) nd (7, 2) 11. (, 2) nd (3, 7) 13 Chpter Skills Prctice

29 Nme Dte 12. (5, 2) nd (0, ) 13. (7, ) nd (2, 9) 1. (5, ) nd (1, 7) 15. (0, 9) nd (5, 2) Chpter Skills Prctice 135

30 16. (, 7) nd (, 5) Use the Distnce Formul to clculte the missing vlue of x. Round your nswer to the nerest tenth, if necessry. 17. The distnce between (1, 2) nd (x, 5) is 5 units. 1. The distnce between (9, 1) nd (x, 7) is 10 units. 136 Chpter Skills Prctice

31 Nme Dte 19. The distnce between (x, ) nd (6, 1) is units. 20. The distnce between (x, 6) nd (7, ) is 7 units. Chpter Skills Prctice 137

32 Use the Distnce Formul to clculte the missing vlue of y. Round your nswer to the nerest tenth, if necessry. 21. The distnce between ( 1, ) nd (5, y) is 10 units. 22. The distnce between (0, 3) nd (6, y) is units. 13 Chpter Skills Prctice

33 Nme Dte 23. The distnce between (10, y) nd ( 2, 2) is 13 units. 2. The distnce between ( 1, y) nd (, 7) is 20 units. Chpter Skills Prctice 139

34 10 Chpter Skills Prctice

35 Skills Prctice Skills Prctice for Lesson.6 Nme Dte Tresure Hunt The Midpoint Formul Vocbulry Identify similrities nd differences between the following terms. 1. midpoint nd men 2. Distnce Formul nd Midpoint Formul Problem Set Divers re mpping the re where ship snk. The coordintes of different lndmrks re given. Plot the coordintes of ech lndmrk on the coordinte grid. 3. (2, 9). (7, 3) y 9 y x x Chpter Skills Prctice 11

36 5. (5, 6) 6. (, 0) y y x x Divers re mpping the re where ship snk on coordinte grid. Determine the midpoint between the pir of lndmrks nd plot the midpoint on the grid. 7. Kerry spots the ship s nchor hlfwy between the lighthouse nd the ledge. Wht re the coordintes of the nchor? y 9 7 ledge rocks lighthouse reef x 12 Chpter Skills Prctice

37 Nme Dte. Erik thinks he will find gold brs hlfwy between the lighthouse nd the reef. Wht re the coordintes of the gold brs? y ledge lighthouse rocks reef x 9. Ilon suspects tht there is chest of gold doubloons t the midpoint between the ledge nd the rocks. At wht coordintes does she think they should serch for the chest? y 9 7 ledge rocks lighthouse reef x Chpter Skills Prctice 13

38 10. Rshid finds one of the ship s cnnons hlfwy between the rocks nd the reef. Wht re the coordintes of the cnnon? y ledge lighthouse rocks reef x 11. The divers gree tht the ship s figurehed is locted t the midpoint between the lighthouse nd the rocks. Wht re the coordintes of the figurehed? y 9 7 ledge rocks lighthouse reef x 1 Chpter Skills Prctice

39 Nme Dte 12. The divers decide to strt their next dive hlfwy between the ledge nd the reef. At wht coordintes will they strt their next dive? y ledge lighthouse rocks reef x Determine the midpoint of the line segment tht hs the given points s its endpoints. Then grph the given points nd the midpoint. 13. (2, ) nd (6, 2) 1. (, 0) nd (, 6) y 9 y x x Chpter Skills Prctice 15

40 15. (9, 3) nd (5, 9) 16. (7, 7) nd (1, 3) y y x x Clculte the midpoint of the line segment tht hs the given points s its endpoints. 17. (, 3) nd (, 9) 1. ( 7, 2) nd ( 3, ) 19. ( 2, 5) nd (10, 7) 20. ( 10, ) nd (6, ) 16 Chpter Skills Prctice

41 Nme Dte 21. (7, 6) nd ( 2, 3) 22. ( 1, ) nd (10, 5) 23. (0, 0) nd (9, 7) 2. ( 5, 6) nd (2, 2) 25. (5, 6) nd ( 6, 5) 26. ( 10, 2) nd (, 3) The coordintes of the endpoint of line segment nd its midpoint re given. Determine the coordintes of the other endpoint. 27. endpoint: (0, 2), midpoint: (3, 3) 2. endpoint: (2, 9), midpoint: (5, 6) Chpter Skills Prctice 17

42 29. endpoint: ( 3, ), midpoint: (0, 1) 30. endpoint: ( 3, 5), midpoint: (1.5, 2) 1 Chpter Skills Prctice

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