Skills Prctice Skills Prctice for Lesson.1 Nme Dte Interior nd Exterior Angles of Tringle Tringle Sum, Exterior Angle, nd Exterior Angle Inequlity Theorems Vocbulry Write the term tht best completes ech sttement. 1. The sttes tht the mesure of n exterior ngle of tringle is greter thn the mesure of either of the remote interior ngles of the tringle. 2. The sttes tht the sum of the mesures of the interior ngles of tringle is 180. 3. The sttes tht the mesure of n exterior ngle of tringle is equl to the sum of the mesures of the remote interior ngles of the tringle.. The re the two ngles tht re non-djcent to the specified exterior ngle. Problem Set Determine the mesure of the missing ngle in ech tringle. 1. A B 78 37 C 2. P 80 66 Q R m B 180 (78 37 ) 65 Chpter Skills Prctice 29
3. K. G 35 M 28 L 90 F 32 E 5. W 6. T 60 110 60 X V 35 U Y List the side lengths from shortest to longest for ech digrm. 7. B 8 c C 8. b 21 r S t A m C 180 (8 21 ) 111 The shortest side of tringle is opposite the smllest ngle. So, the side lengths from shortest to longest re, b, c. T 60 s 5 R 30 Chpter Skills Prctice
Nme Dte 9. k M 10. Z L 28 m 118 K l Y x 2 y 8 X z 11. X b Y 12. 67 79 d c 27 W 6 e Z B u r 50 30 t 60 90 A s D v C Chpter Skills Prctice 31
Identify the interior ngles, the exterior ngle, nd the remote interior ngles of ech tringle. 13. W X Y 1. T U Z Interior ngles: XYZ, YZX, ZXY Exterior ngle: WXZ Remote interior ngles: XYZ, YZX R S 15. F 16. B E G H C A D 17. L J K M 18. R S Q P 32 Chpter Skills Prctice
Nme Dte Solve for x in ech digrm. 19. J 130 F G x 99 H K 20. R x 132 T U 10 S V m GFH 180 130 50 m GHK m GFH m FGH 99 50 x 9 x 21. H x I 2x K J 81 22. U 6 90 (x + 8) R T V S Chpter Skills Prctice 33
23. M 132 J (2x + ) K 2. G 90 F 112 L N D (3x + 2) (2x + 18) E Use the given informtion for ech tringle to write two inequlities tht you would need to prove the Exterior Angle Inequlity Theorem. 25. T 26. Q R P Q R S S Given: Tringle RST with exterior TRQ Prove: m TRQ m S nd m TRQ m T Given: Tringle QRS with exterior PQR Prove: 3 Chpter Skills Prctice
Nme Dte 27. T U 28. J W V F G H Given: Tringle UVW with exterior TUV Prove: Given: Tringle GHJ with exterior FGJ Prove: 29. K L M 30. A B N C D Given: Tringle LMN with exterior KLN Prove: Given: Tringle ABC with exterior BCD Prove: Chpter Skills Prctice 35
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Skills Prctice Skills Prctice for Lesson.2 Nme Dte Instlling Stellite Dish Simplifying Rdicls, Pythgoren Theorem, nd Its Converse Vocbulry Mtch ech definition to its corresponding term. 1. n expression tht involves rdicl sign. squre root 2. the symbol b. rdicl sign 3. number b such tht b 2 c. rdicnd. the sides of right tringle tht form the right ngle d. rdicl expression 5. the expression written under rdicl sign e. simplest form 6. when the rdicnd of rdicl expression f. hypotenuse contins no fctors tht re perfect squres 7. the side opposite the right ngle in right tringle g. legs Chpter Skills Prctice 37
Problem Set Clculte the vlue of ech rdicl expression. 1. 81 2. 121 81 9 2 81 9 3. 16 16. 9 9 5. 16 36 6. 25 100 Simplify ech expression nd write the result in rdicl form. 7. 63 8. 72 63 9 7 9 7 3 7 9. 75 10. 5 11. 300 12. 275 Nme the form of 1 tht you would use to simplify ech frction. 13. 1 5 5 5 1. 7 7 15. 10 3 16. 19 38 Chpter Skills Prctice
Nme Dte Simplify ech frction. 17. 5 6 5 5 6 6 6 5 6 6 6 5 6 6 5 6 36 6 18. 3 5 19. 2 10 20. 6 21. 3 9 22. 6 2 Given the re A of squre, clculte the length of one side. 23. A 8 cm 2 A 2 A 8 16 3 16 3 3 Ech side is 3 centimeters long. Chpter Skills Prctice 39
2. A 75 m 2 25. 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? 26. Devon prepres squre grden with n re of 180 squre feet. How much fencing will Devon need for ech side of the grden? Determine the length of the hypotenuse of ech tringle. Round your nswer to the nerest tenth, if necessry. 27. 3 c c 2 3 2 2 c 2 9 16 c 2 25 c 25 5 The length of the hypotenuse is 5 units. 28. 6 8 c 0 Chpter l Skills Prctice
Nme Dte 29. 8 c 30. 10 c 8 15 Determine the length of the unknown leg. Round your nswer to the nerest tenth, if necessry. 31. 5 13 32. 15 b 12 5 2 b 2 13 2 25 b 2 169 b 2 169 25 b 2 1 b 1 b 12 The length of the unknown leg is 12 units. Chpter l Skills Prctice 1
33. 10 3. 3 9 b 5 Use the converse of the Pythgoren Theorem to determine whether ech tringle is right tringle. Explin your nswer. 35. 8 17 15 Yes. This is right tringle. 8 2 15 2 6 225 289 17 2 The sum of the squres of the lengths of the two legs is equl to the squre of the length of the hypotenuse, so this is right tringle. 2 Chpter l Skills Prctice
Nme Dte 36. 5 9 7 37. 10 8 38. 30 50 0 Chpter Skills Prctice 3
Use the Pythgoren Theorem to clculte ech unknown length. Round your nswer to the nerest tenth, if necessry. 39. 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? 16 2 b 2 20 2 256 b 2 00 b 2 00 256 b 2 1 b 1 b 12 The bse of the ldder is 12 feet from the building. 0. 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? 1. 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? Chpter l Skills Prctice
Nme Dte 2. 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? Chpter Skills Prctice 5
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Skills Prctice Skills Prctice for Lesson.3 Nme Dte Specil Right Tringles Properties of 5 5 90 Tringle Vocbulry Define ech term in your own words. 1. 5 5 90 tringle 2. 5 5 90 Tringle Theorem Problem Set Determine the length of the hypotenuse of ech 5 5 90 tringle. Write your nswer s rdicl in simplest form. 1. 2 in. c 2. 5 cm c 3. 2 in. c 2 2 The length of the hypotenuse is 2 2 inches. 9 ft c. 7 km 5 cm c 9 ft 7 km Chpter Skills Prctice 7
Determine the lengths of the legs of ech 5 5 90 tringle. Write your nswer s rdicl in simplest form. 5. 16 cm 6. 12 mi 2 16 16 2 16 2 2 2 16 2 8 2 2 The length of ech leg is 8 2 centimeters. 7. 6 2 ft 8. 8 2 m Use the given informtion to nswer ech question. Round your nswer to the nerest tenth, if necessry. 9. 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 the ground is the kite? 2 16 16 2 16 2 2 2 16 2 8 2 11.3 2 The kite is pproximtely 11.3 meters bove the ground. 8 Chpter Skills Prctice
Nme Dte 10. 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? 11. 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? 12. 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? Chpter Skills Prctice 9
Determine the re of ech tringle. 13. 16 mm 2 16 16 2 16 2 2 2 16 2 2 8 2 A 1 2 (8 2 )(8 2 ) A 6( 2 ) 2 2 A 6(2) 2 A 6 The re of the tringle is 6 squre millimeters. 1. 18 in. 15. 7 ft 50 Chpter Skills Prctice
Nme Dte 16. 11 m Use the given informtion to nswer ech question. 17. 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 13 13 13( A 1 2( 13 2 2 )( 13 2 2 ) 2 ) 2 2 ( 2 ) 13 A 169( 2 ) 2 169(2) 8 8 2 2 A 169 2.25 The re of ech tile is 2.25 squre centimeters. 18. 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? Chpter Skills Prctice 51
19. Annik is mking kite in the shpe of 5º 5º 90º tringle. The longest side of the kite is 28 inches. Wht is the re of the piece of fbric needed for the kite? 20. 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? 52 Chpter Skills Prctice
Nme Dte Construct ech isosceles tringle described using the given segment. 21. Construct right isosceles tringle ABC with segment BC s the hypotenuse by constructing 5 ngles t B nd C. B C A B C 22. Construct right isosceles tringle WXY with segment WX s the hypotenuse by constructing 5 ngles t W nd X. W X Chpter Skills Prctice 53
23. Construct right isosceles tringle PQR with RQ s leg nd R s the right ngle. R Q 2. Construct right isosceles tringle DEF with DF s leg nd D s the right ngle. D F 5 Chpter Skills Prctice
Skills Prctice Skills Prctice for Lesson. Nme Dte Other Specil Right Tringles Properties of 30 60 90 Tringle Vocbulry Write the term tht best completes ech sttement. 1. A(n) tringle is formed by dividing n equilterl tringle in hlf by its ltitude. 2. The sttes tht the length of the hypotenuse in 30-60 - 90 tringle is two times the length of the shorter leg, nd the length of the longer leg is 3 times the length of the shorter leg. Problem Set Determine the mesure of the indicted interior ngle. 1. A 2. D 30 B C m ABC 60º E G F m DFE 3. H. R 30 J A K S A T m HAK m TRA 60 Chpter Skills Prctice 55
Given the length of the short leg of 30 60 90 tringle, determine the lengths of the long leg nd hypotenuse. Write your nswers s rdicls in simplest form. 5. 3 ft 60 c 6. 60 5 in. c b 30 b 30 3 ft b 3 3 ft c 2(3) 6 ft 7. 60 6 mm b c 30 8. 15 cm 60 c b 30 Given the length of the hypotenuse of 30 60 90 tringle, determine the lengths of the two legs. Write your nswers s rdicls in simplest form. 9. 11. 60 c 20 m 20 m b 30 20 10 m 2 b 10 3 m 60 6 3 yd 10. 12. 60 60 16 km 30 b 2 ft b 30 b 30 56 Chpter Skills Prctice
Nme Dte Given the length of the long side of 30 60 90 tringle, determine the lengths of the short leg nd hypotenuse. Write your nswers s rdicls in simplest form. 13. 60 c 1. 60 c 8 3 in. 30 30 11 3 m b 8 3 in. 8 3 8 in. 3 c 2(8) 16 in. 15. 60 c 16. 60 c 30 12 mi 30 18 ft Determine the re of ech 30 60 90 tringle. Round your nswer to the nerest tenth, if necessry. 17. 60 6 cm b 30 6 3 cm 2 b 3 3 cm A 1 2 3 3 3 A 9 3 7.8 cm2 2 The re of the tringle is pproximtely 7.8 squre centimeters. Chpter Skills Prctice 57
18. 60 12 km b 30 19. 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. 20. 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. 58 Chpter Skills Prctice
Nme Dte Construct ech tringle described using the given segment. 21. Construct 30 60 90 tringle by first constructing n equilterl tringle with MN s side, nd then bisecting one of the sides. M N M N 22. Construct 30 60 90 tringle RST by first constructing n equilterl tringle with RS s side, nd then bisecting the ngle t R. R S Chpter Skills Prctice 59
23. Construct 30 60 90 tringle EFG with EF s the side opposite the 30 ngle by first constructing n equilterl tringle. E F 2. Construct 30 60 90 tringle ABC by first copying ngle A, nd then drwing AB s the hypotenuse. A B A 30 60 Chpter Skills Prctice
Skills Prctice Skills Prctice for Lesson.5 Nme Dte Pst Anyone? Tringle Inequlity Theorem Vocbulry Identify n exmple of ech term in the digrm of tringle ABC. 1. Tringle Inequlity Theorem B 2. uxiliry line A D C Problem Set Without mesuring the ngles, list the ngles of ech tringle in order from lest to gretest mesure. 1. 8 in. F G 11 in. 9 in. H 2..7 cm Y 3.6 cm The smllest ngle of tringle is opposite the shortest side. So, the ngles from lest to gretest re H, F, G. X 2.1 cm W Chpter Skills Prctice 61
3. Q. T 12 in S 8 ft ft 9 in 15 in P 6.3 ft R U 5. F 6. K.6 yd 9.2 yd 5.8 m.2 m E 6 yd G M 5.2 m L Determine whether it is possible to form tringle using ech set of segments with the given mesurements. Explin your resoning. 7. 3 in., 2.9 in., 5 in. 8. 8 ft, 9 ft, 11 ft Yes. Becuse 3 2.9 5.9, nd 5.9 is greter thn 5. 9. m, 5.1 m, 12.5 m 10. 7. cm, 8.1 cm, 9.8 cm 11. 10 yd, 5 yd, 21 yd 12. 13.8 km, 6.3 km, 7.5 km 13. 112 mm, 300 mm, 190 mm 1. 20.2 in., 11 in., 8.2 in. 62 Chpter Skills Prctice
Nme Dte 15. 30 cm, 12 cm, 17 cm 16. 8 ft, 8 ft, 8 ft Write n inequlity tht expresses the possible lengths of the unknown side of ech tringle. 17. Wht could be the length of AB? A 10 m 18. Wht could be the length of DE? 6 cm D B 8 m C AB AC BC AB 10 m 8 m AB 18 m 19. Wht could be the length of HI? I F 9 cm E 20. Wht could be the length of J L? J H 1 in. G 20 in. 12 ft K 7 ft L Chpter Skills Prctice 63
21. Wht could be the length of MN? M 22. Wht could be the length of QR? P N 11 cm O 3 cm 9 mm 13 mm R Q 6 Chpter Skills Prctice