Lesson.1 Skills Practice Name Date Slide, Flip, Turn: The Latest Dance Craze? Translating, Rotating, and Reflecting Geometric Figures Vocabular Match each definition to its corresponding term. 1. rotation a. a line over which a figure is reflected so that corresponding points are the same distance from the line. point of rotation b. the angle measure b which a geometric figure is rotated about the point of rotation 3. angle of rotation c. a rigid motion that turns a figure about a fied point for a given angle and given direction. reflection d. a rigid motion that flips a figure over a given line of reflection 5. line of reflection e. the fied point about which a geometric figure is rotated during a rotation 01 Carnegie Learning Chapter Skills Practice 39
Lesson.1 Skills Practice page Problem Set Transform each given geometric figure on the coordinate plane as described. 1. Translate trapezoid BCD 11 units to the right. B 9 B9 C D D9 0 C9. Translate triangle EFG units up. 0 E F G 01 Carnegie Learning 0 Chapter Skills Practice
Lesson.1 Skills Practice page 3 Name Date 3. Rotate rectangle HJKL about the origin 90 counterclockwise. H J L K 0. Rotate triangle MNP about the origin 10 counterclockwise. 0 N 01 Carnegie Learning M P Chapter Skills Practice 1
Lesson.1 Skills Practice page 5. Rotate trapezoid QRST about the origin 90 counterclockwise. 0 R S Q T. Rotate parallelogram WXYZ about the origin 10 counterclockwise. X Y W 0 Z 01 Carnegie Learning Chapter Skills Practice
Lesson.1 Skills Practice page 5 Name Date 7. Reflect triangle BC over the -ais. B C 0. Reflect parallelogram DEFG over the -ais. 0 01 Carnegie Learning D E G F Chapter Skills Practice 3
Lesson.1 Skills Practice page 9. Reflect trapezoid HJKL over the -ais. J K H 0 L 10. Reflect quadrilateral MNPQ over the -ais. 0 N P M Q 01 Carnegie Learning Chapter Skills Practice
Lesson.1 Skills Practice page 7 Name Date Determine the coordinates of each translated image without graphing. 11. The vertices of triangle BC are (5, 3), B (, ), and C (, 5). Translate the triangle units to the left to form triangle B C. The vertices of triangle B C are (1, 3), B (, ), and C (10, 5). 1. The vertices of rectangle DEFG are D (7, 1), E (7, ), F (1, ), and G (1, 1). Translate the rectangle 10 units down to form rectangle D E F G.. The vertices of parallelogram HJKL are H (, ), J (3, 1), K (7, 1), and L (, ). Translate the parallelogram 7 units up to form parallelogram H J K L. 1. The vertices of trapezoid MNPQ are M (, 5), N (0, 5), P (1, ), and Q (, ). Translate the trapezoid units to the right to form trapezoid M N P Q. 15. The vertices of triangle RST are R (0, 3), S (, 7), and T (3, 1). Translate the triangle 5 units to the left and 3 units up to form triangle R S T. 1. The vertices of quadrilateral WXYZ are W (10, ), X (, 1), Y (0, 0), and Z (3, 7). Translate the quadrilateral 5 units to the right and units down to form quadrilateral W X Y Z. 01 Carnegie Learning Determine the coordinates of each rotated image without graphing. 17. The vertices of triangle BC are (5, 3), B (, ), and C (, 5). Rotate the triangle about the origin 90 counterclockwise to form triangle B C. The vertices of triangle B C are (3, 5), B (, ), and C (5, ). 1. The vertices of rectangle DEFG are D (7, 1), E (7, ), F (1, ), and G (1, 1). Rotate the rectangle about the origin 10 counterclockwise to form rectangle D E F G. Chapter Skills Practice 5
Lesson.1 Skills Practice page 19. The vertices of parallelogram HJKL are H (, ), J (3, 1), K (7, 1), and L (, ). Rotate the parallelogram about the origin 90 counterclockwise to form parallelogram H J K L. 0. The vertices of trapezoid MNPQ are M (, 5), N (0, 5), P (1, ), and Q (, ). Rotate the trapezoid about the origin 10 counterclockwise to form trapezoid M N P Q. 1. The vertices of triangle RST are R (0, 3), S (, 7), and T (3, 1). Rotate the triangle about the origin 90 counterclockwise to form triangle R S T.. The vertices of quadrilateral WXYZ are W (10, ), X (, 1), Y (0, 0), and Z (3, 7). Rotate the quadrilateral about the origin 10 counterclockwise to form quadrilateral W X Y Z. Determine the coordinates of each reflected image without graphing. 3. The vertices of triangle BC are (5, 3), B (, ), and C (, 5). Reflect the triangle over the -ais to form triangle B C. The vertices of triangle B C are (5, 3), B (, ), and C (, 5).. The vertices of rectangle DEFG are D (7, 1), E (7, ), F (1, ), and G (1, 1). Reflect the rectangle over the -ais to form rectangle D E F G. 5. The vertices of parallelogram HJKL are H (, ), J (3, 1), K (7, 1), and L (, ). Reflect the parallelogram over the -ais to form parallelogram H J K L.. The vertices of trapezoid MNPQ are M (, 5), N (0, 5), P (1, ), and Q (, ). Reflect the trapezoid over the -ais to form trapezoid M N P Q. 7. The vertices of triangle RST are R (0, 3), S (, 7), and T (3, 1). Reflect the triangle over the -ais to form triangle R S T. 01 Carnegie Learning. The vertices of quadrilateral WXYZ are W (10, ), X (, 1), Y (0, 0), and Z (3, 7). Reflect the quadrilateral over the -ais to form quadrilateral W X Y Z. Chapter Skills Practice
Lesson. Skills Practice Name Date ll the Same to You Congruent Triangles Vocabular Complete each problem related to the ke terms of the lesson. 1. Draw and label a pair of congruent triangles. Write a congruence statement for the triangles. a. Identif each pair of congruent line segments in the drawing. b. Identif each pair of congruent angles in the drawing. c. Identif each pair of corresponding sides in the drawing. 01 Carnegie Learning d. Identif each pair of corresponding angles in the drawing. Chapter Skills Practice 7
Lesson. Skills Practice page Problem Set Identif the transformation used to create nxyz on each coordinate plane. Identif the congruent angles and the congruent sides. Then write a triangle congruence statement. 1. Triangle BC was reflected over the -ais to create triangle XYZ. BC > XY, C > YZ, and B > XZ ; /B > /X, /C > /Y, and / > /Z. B 0 X C Y nbc > nxyz Z. X Z Y 0 D E F 01 Carnegie Learning Chapter Skills Practice
Lesson. Skills Practice page 3 Name Date 3. P M T 0 Z X Y. B D X Z N 0 Y 01 Carnegie Learning Chapter Skills Practice 9
Lesson. Skills Practice page 5. Y X Z 0 F W. Z X 0 M Y Q R 01 Carnegie Learning 50 Chapter Skills Practice
Lesson. Skills Practice page 5 Name Date 7. Y Z N G X 0 R. Y X Z 0 W 01 Carnegie Learning H F Chapter Skills Practice 51
Lesson. Skills Practice page 9. T Y Z V X 0 10. M B 0 Y X Z G 01 Carnegie Learning 5 Chapter Skills Practice
Lesson. Skills Practice page 7 Name Date List the corresponding sides and angles using congruence smbols for each pair of triangles represented b the given congruence statement. 11. njpm > ntrw JP > TR, PM > RW, and JM > TW ; /J > /T, /P > /R, and /M > /W. 1. neu > nbcd. nluv > nmth 1. nrwb > nvcq 15. ntom > nben 1. njkl > nrst 17. nct > nsup 1. ntop > ngun 01 Carnegie Learning Chapter Skills Practice 53
01 Carnegie Learning 5 Chapter Skills Practice
Lesson.3 Skills Practice Name Date Side-Side-Side SSS Congruence Theorem Vocabular Define each term in our own words. 1. theorem. postulate 3. Side-Side-Side (SSS) Congruence Theorem 01 Carnegie Learning Chapter Skills Practice 55
Lesson.3 Skills Practice page Problem Set Determine whether each pair of given triangles are congruent b SSS. Use the Distance Formula when necessar. 1. B 5 DE 5 3 C 5 DF 5 7 B d 5 ( 1 ) 1 ( 1 ) C BC 5 ( 9 ) 1 ( 7 ) BC 5 7 1 ( 3) 0 BC 5 9 1 9 F D BC 5 5 < 7. E d 5 ( 1 ) 1 ( 1 ) EF 5 ( 1 ) 1 ( 3 () ) EF 5 ( 7 ) 1 3 EF 5 9 1 9 EF 5 5 < 7. BC 5 EF The triangles are congruent b the SSS Congruence Theorem. 01 Carnegie Learning 5 Chapter Skills Practice
Lesson.3 Skills Practice page 3 Name Date. J G H 0 L K M 01 Carnegie Learning Chapter Skills Practice 57
Lesson.3 Skills Practice page 3. B R G 0 D M 01 Carnegie Learning 5 Chapter Skills Practice
Lesson.3 Skills Practice page 5 Name Date. P M N 0 Y X Z 01 Carnegie Learning Chapter Skills Practice 59
Lesson.3 Skills Practice page 5. C M W 0 Q P S 01 Carnegie Learning 0 Chapter Skills Practice
Lesson.3 Skills Practice page 7 Name Date. N P Q 0 T S R 01 Carnegie Learning Chapter Skills Practice 1
Lesson.3 Skills Practice page Perform the transformation described on each given triangle. Then verif that the triangles are congruent b SSS. Use the Distance Formula when necessar. 7. Reflect nbc over the -ais to form nxyz. Verif that nbc > nbc b SSS. B 5 XY 5 1 0 B C Z X Y BC 5 YZ 5 5 d 5 ( 1 ) 1 ( 1 ) C 5 ( (9) ) 1 ( ) C 5 5 1 ( 1 ) C 5 5 1 1 C 5 19 5 d 5 ( 1 ) 1 ( 1 ) XZ 5 ( 9 ) 1 ( ) XZ 5 ( 5 ) 1 ( 1 ) XZ 5 5 1 1 XZ 5 19 5 C 5 XZ The triangles are congruent b the SSS Congruence Theorem. 01 Carnegie Learning Chapter Skills Practice
Lesson.3 Skills Practice page 9 Name Date. Rotate ndef 10 clockwise to form nqrs. Verif that ndef > nqrs b SSS. D E F 0 01 Carnegie Learning Chapter Skills Practice 3
Lesson.3 Skills Practice page 10 9. Reflect njkl over the -ais to form nmnp. Verif that njkl > nmnp b SSS. 0 J K L 01 Carnegie Learning Chapter Skills Practice
Lesson.3 Skills Practice page 11 Name Date 10. Translate nhmz 10 units to the left and 1 unit down to form nbny. Verif that nhmz > nbny b SSS. H M 0 Z 01 Carnegie Learning Chapter Skills Practice 5
Lesson.3 Skills Practice page 1 11. Rotate nfp 90 counterclockwise to form ndhw. Verif that nfp > ndhw b SSS. F 0 P 01 Carnegie Learning Chapter Skills Practice
Lesson.3 Skills Practice page Name Date 1. Translate nce 3 units to the right and 9 units up to form njkq. Verif that nce > njkq b SSS. 0 C E 01 Carnegie Learning Chapter Skills Practice 7
01 Carnegie Learning Chapter Skills Practice
Lesson. Skills Practice Name Date Side-ngle-Side SS Congruence Theorem Vocabular Describe how to prove the given triangles are congruent. Use the ke terms included angle and Side-ngle-Side Congruence Theorem in our answer. 1. C B 0 X Z Y 01 Carnegie Learning Chapter Skills Practice 9
Lesson. Skills Practice page Problem Set Determine whether each pair of given triangles are congruent b SS. Use the Distance Formula when necessar. 1. Determine whether nbc is congruent to ndef b SS. B 5 DE 5 5 BC 5 EF 5 7 m/b 5 m/e 5 90 The triangles are congruent b the SS Congruence Theorem. B C 0 F E D. Determine whether ncky is congruent to ndlz b SS. C L Z 0 Y K D 01 Carnegie Learning 70 Chapter Skills Practice
Lesson. Skills Practice page 3 Name Date 3. Determine whether nfmr is congruent to njqw b SS. M F W 0 R Q J. Determine whether nqrs is congruent to nxyz b SS. Q R 01 Carnegie Learning S 0 Y Z X Chapter Skills Practice 71
Lesson. Skills Practice page 5. Determine whether njkl is congruent to nmnp b SS. J K L 0 P N M 01 Carnegie Learning 7 Chapter Skills Practice
Lesson. Skills Practice page 5 Name Date. Determine whether ntv is congruent to ndnp b SS. T 0 V N D P 01 Carnegie Learning Chapter Skills Practice 73
Lesson. Skills Practice page Perform the transformation described on each given triangle. Then verif that the triangles are congruent b SS. Use the Distance Formula when necessar. 7. Reflect nbc over the -ais to form nxyz. Verif that nbc > nxyz b SS. B 5 XY 5 5 B Y X C 5 XZ 5 5 m/ 5 m/x 5 90 The triangles are congruent b the SS Congruence Theorem. C Z 0. Translate ndef 11 units to the left and 10 units down to form nqrs. Verif that ndef > nqrs b SS. D F E 0 01 Carnegie Learning 7 Chapter Skills Practice
Lesson. Skills Practice page 7 Name Date 9. Rotate njkl 10 counterclockwise to form nmnp. Verif that njkl > nmnp b SS. 0 L J K 10. Reflect nfp over the -ais to form ndhw. Verif that nfp > ndhw b SS. F 01 Carnegie Learning 0 P Chapter Skills Practice 75
Lesson. Skills Practice page 11. Translate nce units to the right and units down to form njkq. Verif that nce > njkq b SS. E C 0 01 Carnegie Learning 7 Chapter Skills Practice
Lesson. Skills Practice page 9 Name Date 1. Rotate nbmz 90 counterclockwise to form ndrt. Verif that nbmz > ndrt b SS. B M Z 0 01 Carnegie Learning Chapter Skills Practice 77
Lesson. Skills Practice page 10 Determine the angle measure or side measure that is needed in order to prove that each set of triangles are congruent b SS.. In nrt, R 5 1, RT 5, and m/r 5 70. In nbsw, BS 5 1 and m/s 5 70. SW 5 1. In ncde, CD 5 7, DE 5 11, In nfgh, FG 5 7, GH 5 11 and m/g 5 5. 15. In njkl, JK 5, KL 5 3, and m/k 5 0. In nmnp, NP 5 3 and m/n 5 0. 1. In nqrs, QS 5, RS 5, and m/s 5 0. In ntuv, TV 5 and UV 5. 17. T Z 11 in. D 15 in. 15 in. B 5 11 in. W R 1. K L ft ft T M X 0 ft N 01 Carnegie Learning 7 Chapter Skills Practice
Lesson. Skills Practice page 11 Name Date 19. C 7 m O 7 m 50 G m m T D 0. V E 35 1 ft R P 1 ft 1 ft W 35 M 01 Carnegie Learning Chapter Skills Practice 79
Lesson. Skills Practice page 1 Determine whether there is enough information to prove that each pair of triangles are congruent b SSS or SS. Write the congruence statements to justif our reasoning. 1. nmnp >? npqm. nwxy >? nzyx 1 in. N 10 in. W 30 X M P 7 ft 7 ft 10 in. 1 in. Y 30 Z Q The triangles are congruent b SSS. MN > PQ NP > QM MP > PM 3. nbce >? ndf. nhjm >? nmkh B J K cm E F cm C H M D 01 Carnegie Learning 0 Chapter Skills Practice
Lesson. Skills Practice page Name Date 5. npqr >? nstw. nmt >? nmht Q S T R M T P W H 7. nbdw >? nbrn. nbc >? nedc 5 m D 3 m N B B C 5 m R 3 m W E D 01 Carnegie Learning Chapter Skills Practice 1
01 Carnegie Learning Chapter Skills Practice
Lesson.5 Skills Practice Name Date You Shouldn t Make ssumptions ngle-side-ngle Congruence Theorem Vocabular Describe how to prove the given triangles are congruent. Use the ke terms included side and ngle-side-ngle Congruence Theorem in our answer. 1. P N M 0 C B 01 Carnegie Learning Chapter Skills Practice 3
Lesson.5 Skills Practice page Problem Set Determine whether each pair of given triangles are congruent b S. 1. Determine whether nbc is congruent to ndef b S. B C m/b 5 m/e 5 90 m/c 5 m/f 5 5 BC 5 EF 5 5 The triangles are congruent b the S Congruence Theorem. 0 E D F. Determine whether nnpq is congruent to nrst b S. N Q P 0 S R T 01 Carnegie Learning Chapter Skills Practice
Lesson.5 Skills Practice page 3 Name Date 3. Determine whether ngp is congruent to nbhq b S. P G 0 Q H B. Determine whether ncky is congruent to ndlz b S. Z C K 01 Carnegie Learning 0 D L Y Chapter Skills Practice 5
Lesson.5 Skills Practice page 5. Determine whether nfmr is congruent to njqw b S. M F 0 J W R Q. Determine whether nghj is congruent to nklm b S. G H L 0 J M K 01 Carnegie Learning Chapter Skills Practice
Lesson.5 Skills Practice page 5 Name Date Perform the transformation described on each given triangle. Then verif that the triangles are congruent b S. 7. Reflect nbc over the -ais to form nxyz. Verif that nbc > nxyz b SS. m/c 5 m/z 5 90 m/ 5 m/x 5 3 C 5 XZ 5 3 The triangles are congruent b the S Congruence Theorem. 0 X Y Z C B. Rotate ndef 90 counterclockwise to form nqrs. Verif that ndef > nqrs b SS. D 01 Carnegie Learning E F 0 Chapter Skills Practice 7
Lesson.5 Skills Practice page 9. Translate nhmz units to the right and 10 units up to form nbny. Verif that nhmz > nbny b S. 0 H M Z 10. Reflect nfp over the -ais to form ndhw. Verif that nfp > ndhw b S. F 0 P 01 Carnegie Learning Chapter Skills Practice
Lesson.5 Skills Practice page 7 Name Date 11. Rotate nce 10 counterclockwise to form njkq. Verif that nce > njkq b SS. C 0 E 1. Reflect njkl over the -ais to form nmnp. Verif that njkl > nmnp b S. J K L 01 Carnegie Learning 0 Chapter Skills Practice 9
Lesson.5 Skills Practice page Determine the angle measure or side measure that is needed in order to prove that each set of triangles are congruent b S.. In ndz, m/ 5 0, D 5 9, and m/d 5 70. In nben, BE 5 9 and m/e 5 70. m/b 5 0 1. In ncup, m/u 5 5, and m/p 5 55, In nht, T 5 1, m/ 5 5. and m/t 5 55. 15. In nhow, m/h 5 10, HW 5 3, and m/w 5 0. In nfr, FR 5 3 and m/f 5 10. 1. In ndry, m/d 5 100, DR 5 5, and m/r 5 30, In nwet, m/w 5 100 and m/e 5 30. 17. B D W 0 ft T R ft Z 1. K M 30 7 in. 0 T L 30 0 X N 01 Carnegie Learning 90 Chapter Skills Practice
Lesson.5 Skills Practice page 9 Name Date 19. R G F 0 1 m 1 m 70 W 70 Z S 0. 0 P T 5 in. 5 5 0 X D M 01 Carnegie Learning Chapter Skills Practice 91
01 Carnegie Learning 9 Chapter Skills Practice
Lesson. Skills Practice Name Date hhhhh... We re Sorr We Didn t Include You! ngle-ngle-side Congruence Theorem Vocabular Describe how to prove the given triangles are congruent. Use the ke terms non-included side and ngle-ngle-side Congruence Theorem in our answer. 1. B C 0 X Z Y 01 Carnegie Learning Chapter Skills Practice 93
Lesson. Skills Practice page Problem Set Determine whether each set of given triangles are congruent b S. 1. Determine whether nbc is congruent to ndef b S. C B 0 D F Methods ma var. m/ 5 m/d 5 5 m/b 5 m/e 5 5 BC 5 EF 5 7 The triangles are congruent b the S Congruence Theorem. E. Determine whether nghj is congruent to nklm b S. G J H 0 L M K 01 Carnegie Learning 9 Chapter Skills Practice
Lesson. Skills Practice page 3 Name Date 3. Determine whether ngp is congruent to nbhq b S. G Q B 0 P H. Determine whether ncky is congruent to ndlz b S. C Y K 0 L Z 01 Carnegie Learning D Chapter Skills Practice 95
Lesson. Skills Practice page 5. Determine whether nfmr is congruent to njqw b S. F M 0 W R Q J. Determine whether nnpq is congruent to nrst b S. P T N 0 R Q S 01 Carnegie Learning 9 Chapter Skills Practice
Lesson. Skills Practice page 5 Name Date Perform the transformation described on each given triangle. Then verif that the triangles are congruent b S. 7. Reflect nbc over the -ais to form nxyz. Verif that nbc > nxyz b S. Methods ma var. X m/b 5 m/y 5 7 m/c 5 m/z 5 90 C 5 XZ 5 1 The triangles are congruent b the S Congruence Theorem. 0 Y Z C B. Translate ndef 11 units to the left and 11 units down to form nqrs. Verif that ndef > nqrs b S. D 01 Carnegie Learning F 0 E Chapter Skills Practice 97
Lesson. Skills Practice page 9. Rotate njkl 10 counterclockwise to form nmnp. Verif that njkl > nmnp b S. 0 K L J 10. Translate ncup 9 units to the left and units up to form njr. Verif that ncup > njr b S. 0 U C P 01 Carnegie Learning 9 Chapter Skills Practice
Lesson. Skills Practice page 7 Name Date 11. Reflect nfp over the -ais to form ndhw. Verif that nfp > ndhw b S. 0 F P 01 Carnegie Learning Chapter Skills Practice 99
Lesson. Skills Practice page 1. Rotate nce 70 counterclockwise to form njkq. Verif that nce > njkq b S. C 0 E Determine the angle measure or side measure that is needed in order to prove that each set of triangles are congruent b S.. In nnt, m/ 5 30, m/n 5 0, and NT 5 5. In nbug, m/u 5 0 and UG 5 5. m/b 5 30 1. In nbcd, m/b 5 5, and m/d 5 105. In nrst, RS 5 1, m/r 5 5, and m/t 5 105. 15. In nemz, m/e 5 0, EZ 5 7, and m/m 5 70. In ndgp, DP 5 7 and m/d 5 0. 1. In nbmx, m/m 5 90, BM 5 1, and m/x 5 15. In ncny, m/n 5 90 and m/y 5 15. 01 Carnegie Learning 700 Chapter Skills Practice
Lesson. Skills Practice page 9 Name Date 17. B D 1 in. 1 in. 0 T R 0 70 W Z 1. K 0 X 30 N T 3 ft 30 M 0 L 19. F S 50 0 W 01 Carnegie Learning Z 0 50 R 5 m G Chapter Skills Practice 701
Lesson. Skills Practice page 10 0. D 0 in. 110 30 P M 30 0 in. X T Determine whether there is enough information to prove that each pair of triangles are congruent b S or S. Write the congruence statements to justif our reasoning.? 1. nbd > ncbd?. nefg > nhjk B F J D The triangles are congruent b S. /BD > /BCD C E K G H /DB > /CDB BD > BD? 3. nmnq > npqn?. nrst > nwzt N P W M Q S R T Z 01 Carnegie Learning 70 Chapter Skills Practice
Lesson. Skills Practice page 11 Name Date? 5. nbdm > nmdh?. nfgh > njhg D F J 55 55 B 0 H 0 M G H? 7. ndfg > njmt?. nrst > nwxy D M 5 T 50 S W R ft F 5 G ft J 70 T 3 cm X 50 3 cm 70 Y 01 Carnegie Learning Chapter Skills Practice 703
01 Carnegie Learning 70 Chapter Skills Practice