Skills Practice Skills Practice for Lesson 4.1


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1 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 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 nondjcent to the specified exterior ngle. Problem Set Determine the mesure of the missing ngle in ech tringle. 1. A B C 2. P Q R m B 180 (78 37 ) 65 Chpter Skills Prctice 29
2 3. K. G 35 M 28 L 90 F 32 E 5. W 6. T 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
3 Nme Dte 9. k M 10. Z L 28 m 118 K l Y x 2 y 8 X z 11. X b Y d c 27 W 6 e Z B u r t A s D v C Chpter Skills Prctice 31
4 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
5 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 m GHK m GFH m FGH x 9 x 21. H x I 2x K J U 6 90 (x + 8) R T V S Chpter Skills Prctice 33
6 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
7 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
8 36 Chpter Skills Prctice
9 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
10 Problem Set Clculte the vlue of ech rdicl expression Simplify ech expression nd write the result in rdicl form Nme the form of 1 tht you would use to simplify ech frction Chpter Skills Prctice
11 Nme Dte Simplify ech frction Given the re A of squre, clculte the length of one side. 23. A 8 cm 2 A 2 A Ech side is 3 centimeters long. Chpter Skills Prctice 39
12 2. A 75 m 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 c c c c 2 25 c 25 5 The length of the hypotenuse is 5 units c 0 Chpter l Skills Prctice
13 Nme Dte c c 8 15 Determine the length of the unknown leg. Round your nswer to the nerest tenth, if necessry b b b b b 2 1 b 1 b 12 The length of the unknown leg is 12 units. Chpter l Skills Prctice 1
14 b 5 Use the converse of the Pythgoren Theorem to determine whether ech tringle is right tringle. Explin your nswer Yes. This is right tringle 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
15 Nme Dte Chpter Skills Prctice 3
16 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 b 2 00 b 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
17 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
18 6 Chpter Skills Prctice
19 Skills Prctice Skills Prctice for Lesson.3 Nme Dte Specil Right Tringles Properties of Tringle Vocbulry Define ech term in your own words tringle Tringle Theorem Problem Set Determine the length of the hypotenuse of ech tringle. Write your nswer s rdicl in simplest form 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
20 Determine the lengths of the legs of ech tringle. Write your nswer s rdicl in simplest form cm mi The length of ech leg is 8 2 centimeters ft 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? The kite is pproximtely 11.3 meters bove the ground. 8 Chpter Skills Prctice
21 Nme Dte 10. Meen is picking ornges from the tree in her yrd. She rests 12foot 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
22 Determine the re of ech tringle mm 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 in ft 50 Chpter Skills Prctice
23 Nme Dte 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? ( A 1 2( )( ) 2 ) 2 2 ( 2 ) 13 A 169( 2 ) 2 169(2) A 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
24 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
25 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
26 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
27 Skills Prctice Skills Prctice for Lesson. Nme Dte Other Specil Right Tringles Properties of 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 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
28 Given the length of the short leg of tringle, determine the lengths of the long leg nd hypotenuse. Write your nswers s rdicls in simplest form ft 60 c in. c b 30 b 30 3 ft b 3 3 ft c 2(3) 6 ft mm b c cm 60 c b 30 Given the length of the hypotenuse of tringle, determine the lengths of the two legs. Write your nswers s rdicls in simplest form c 20 m 20 m b m 2 b 10 3 m yd km 30 b 2 ft b 30 b Chpter Skills Prctice
29 Nme Dte Given the length of the long side of tringle, determine the lengths of the short leg nd hypotenuse. Write your nswers s rdicls in simplest form c c 8 3 in m b 8 3 in in. 3 c 2(8) 16 in c c mi ft Determine the re of ech tringle. Round your nswer to the nerest tenth, if necessry cm b cm 2 b 3 3 cm A A cm2 2 The re of the tringle is pproximtely 7.8 squre centimeters. Chpter Skills Prctice 57
30 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. 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
31 Nme Dte Construct ech tringle described using the given segment. 21. Construct tringle by first constructing n equilterl tringle with MN s side, nd then bisecting one of the sides. M N M N 22. Construct 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
32 23. Construct tringle EFG with EF s the side opposite the 30 ngle by first constructing n equilterl tringle. E F 2. Construct tringle ABC by first copying ngle A, nd then drwing AB s the hypotenuse. A B A Chpter Skills Prctice
33 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 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
34 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 in., 2.9 in., 5 in ft, 9 ft, 11 ft Yes. Becuse , nd 5.9 is greter thn m, 5.1 m, 12.5 m cm, 8.1 cm, 9.8 cm yd, 5 yd, 21 yd km, 6.3 km, 7.5 km mm, 300 mm, 190 mm in., 11 in., 8.2 in. 62 Chpter Skills Prctice
35 Nme Dte cm, 12 cm, 17 cm 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
36 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
Skills Practice Skills Practice for Lesson 4.1
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
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