Lesson 8.1 Skills Practice

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1 Lesson.1 Skills Practice Name Date Slide, Flip, Turn! Translations, Rotations, and Reflections of Triangles Problem Set Perform each given transformation. 1. Translate nabc units to the right and 9 units down. B A C B' A' C' Chapter Skills Practice 3

2 Lesson.1 Skills Practice page. Rotate ndef 9 counterclockwise about the origin. E D F Reflect nfgh over the -ais G - - F H Chapter Skills Practice

3 Lesson.1 Skills Practice page 3 Name Date. Translate njkl 1 units to the right and 5 units up J K L 5. Rotate nmnp 9 clockwise about the origin. N M P Chapter Skills Practice 5

4 Lesson.1 Skills Practice page. Reflect nqrs over the -ais. Q R S Translate ntuv units to the left and units up U - - T V Chapter Skills Practice

5 Lesson.1 Skills Practice page 5 Name Date. Rotate nxyz 1 counterclockwise about the origin. Y Z X Reflect nabc over the -ais. A B C Chapter Skills Practice 7

6 Lesson.1 Skills Practice page 1. Rotate nabc 9 counterclockwise about the origin A - - B C Determine the coordinates of the triangle s image after each given transformation. 11. Triangle ABC with coordinates A(3, ), B(7, 7), and C(, 1) is translated units left and 7 units down. The coordinates of the image are A9(3, 3), B9(1, ), and C9(, ). 1. Triangle DEF with coordinates D(, ), E(1, 5), and F(, 1) is rotated 9 counterclockwise about the origin. 13. Triangle GHJ with coordinates G(, 9), H(3, ), and J(1, ) is reflected over the -ais. 1. Triangle KLM with coordinates K(, ), L(, 7), and M(3, 3) is translated units right and 9 units up. 15. Triangle NPQ with coordinates N(1, 3), P(1, ), and Q(9, ) is rotated 1 counterclockwise about the origin. Chapter Skills Practice

7 Lesson.1 Skills Practice page 7 Name Date 1. Triangle RST with coordinates R(, 9), S(5, 7), and T(11, ) is reflected over the -ais. 17. Triangle WXY with coordinates W(, ), X(5, 15), and Y(, 3) is translated units left and 15 units up. 1. Triangle ABC with coordinates A(, ), B(1, 5), and C(, 1) is rotated 9 clockwise about the origin. 19. Triangle DMP with coordinates D(1, 15), M(5, ), and P(, 1) is reflected over the -ais.. Triangle XYZ with coordinates X(1, 1), Y(, ), and Z(1, 9) is rotated 9 counterclockwise about the origin. Describe the transformation used to form each triangle. 1. The vertices of triangle ABC are A(, ), B(5, 7), and C(3, 1). Describe the translation used to form triangle A9B9C9 for A9(5, ), B9(, 7), and C9(, 1). Triangle A9B9C9 was formed b translating triangle ABC 7 units to the left.. The vertices of triangle DEF are D(, 3), E(1, ), and F(3, ). Describe the rotation used to form triangle D9E9F9 for D9(3, ), E9(, 1), and F9(, 3). 3. The vertices of triangle GHJ are G(5, 3), H(, ), and J(, ). Describe the reflection used to form triangle G9H9J9 for G9(5, 3), H9(, ), and J9(, ). Chapter Skills Practice 9

8 Lesson.1 Skills Practice page. The vertices of triangle KMN are K(1, 3), M(5, ), and N(, ). Describe the translation used to form triangle K9M9N9 for K9(1, ), M9(1, 1), and N9(1, 7). 5. The vertices of triangle PQR are P(9, ), Q(1, ), and R(7, 3). Describe the rotation used to form triangle P9Q9R9 for P9(9, ), Q9(1, ), and R9(7, 3).. The vertices of triangle STW are S(15, ), T(, 3), and W(, ). Describe the reflection used to form triangle S9T9W9 for S9(15, ), T9(, 3), and W9(, ). 7. The vertices of triangle XYZ are X(, ), Y(5, 9), and Z(1, 5). Describe the translation used to form triangle X9Y9Z9 for X9(, 1), Y9(15, ), and Z9(, ).. The vertices of triangle ANW are A(, 9), N(, ), and W(, 1). Describe the rotation used to form triangle A9N9W9 for A9(9, ), N9(, ), and W9(1, ). 9. The vertices of triangle BGZ are B(11, ), G(, 7), and Z(, ). Describe the reflection used to form triangle B9G9Z9 for B9(11, ), G9(, 7), and Z9(, ). 3. The vertices of triangle DMV are D(3, 1), M(1, 11), and V(3, ). Describe the translation used to form triangle D9M9V9 for D9(, ), M9(, 1), and V9(, 1). 5 Chapter Skills Practice

9 Lesson. Skills Practice Name Date All the Same to You Congruent Triangles Vocabular Answer 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.. Identif each pair of congruent line segments in the drawing ou made for Problem Identif each pair of congruent angles in the drawing ou made for Problem 1.. Identif each pair of corresponding sides in the drawing ou made for Problem Identif each pair of corresponding angles in the drawing ou made for Problem 1. Chapter Skills Practice 51

10 Lesson. Skills Practice page Problem Set Identif the transformation used to create nxyz in each. List the corresponding sides and angles of the congruent triangles using congruence smbols and write a congruence statement. 1. A Triangle BCA was reflected over the -ais to create triangle XYZ. B C BC > XY, CA > YZ, and BA > XZ ; /B > /X, /C > /Y, and /A > /Z X Y nbca > nxyz - - Z. X Z Y D - - E F 5 Chapter Skills Practice

11 Lesson. Skills Practice page 3 Name Date 3. P M T Z X Y. B D X Z N Y Chapter Skills Practice 53

12 Lesson. Skills Practice page 5. Y X Z F - A W -. Z X Y Q - M - R 5 Chapter Skills Practice

13 Lesson. Skills Practice page 5 Name Date 7. N R Y Z X G Y X Z H F W Chapter Skills Practice 55

14 Lesson. Skills Practice page 9. A T Y Z V X M X B Y - - G Z - 5 Chapter Skills Practice

15 Lesson. Skills Practice page 7 Name Date List the corresponding sides and angles using congruence smbols for each of the 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. naeu > nbcd 13. nluv > nmth 1. nrwb > nvcq 15. ntom > nben 1. njkl > nrst 17. ncat > nsup 1. ntop > ngun Chapter Skills Practice 57

16 5 Chapter Skills Practice

17 Lesson.3 Skills Practice Name Date Two Was to Tell SSS and SAS Congruence Vocabular Define each term in our own words. 1. SSS Congruence Theorem. included angle 3. SAS Congruence Theorem Chapter Skills Practice 59

18 Lesson.3 Skills Practice page Problem Set Determine whether each of the given triangles are congruent. 1. Determine whether nabc is congruent to ndef b SSS. a 1 b 5 c a 1 b 5 c BC EF BC EF 5 5 BC 5 5 EF 5 5 BC 5 5 EF B A F - C - - D E BC 5 EF 5 5, AC 5 DF 5 7, and AB 5 DE 5 3. The triangles are congruent b the SSS Congruence Theorem. Chapter Skills Practice

19 Lesson.3 Skills Practice page 3 Name Date. Determine whether njkl is congruent to nmnp b SSS. K J L M P N Chapter Skills Practice 1

20 Lesson.3 Skills Practice page 3. Determine whether nabc is congruent to nxyz b SSS. A B C Y - - X Z Chapter Skills Practice

21 Lesson.3 Skills Practice page 5 Name Date. Determine whether nmnp is congruent to nqrs b SSS. N M P Q S - - R Chapter Skills Practice 3

22 Lesson.3 Skills Practice page 5. Determine whether nabc is congruent to nrst b SAS. B A C S T - - R. Determine whether ndef is congruent to njmn b SAS. N J E D M - F Chapter Skills Practice

23 Lesson.3 Skills Practice page 7 Name Date 7. Determine whether nrst is congruent to nwxy b SAS. R S T W - X - - Y. Determine whether nbdg is congruent to njpx b SAS. D P B G X J Chapter Skills Practice 5

24 Lesson.3 Skills Practice page Determine whether each of the given triangles are congruent b SSS or SAS. If there is not enough information to determine whether the triangles are congruent, write not enough information. 9. nabc > ndcb B A D C The triangles are congruent b SSS. 1. nefg > nhjk E G J F K H 11. nmnp > nqrs M Q m m N 1 m P S 1 m R Chapter Skills Practice

25 Lesson.3 Skills Practice page 9 Name Date 1. ntvw > nxyz 7 in. V 1 in. Z 1 in. X T 1 in. W 1 in. Y 7 in. 13. nadg > nmgd A D G M 1. nkpt > nkwt P K 5 ft T 5 ft W Chapter Skills Practice 7

26 Lesson.3 Skills Practice page nabc > nxyz A X B C Y Z 1. ndef > nrst D cm E T 7 cm R 7 cm cm 7 cm cm F S Chapter Skills Practice

27 Lesson.3 Skills Practice page 11 Name Date 17. nabd > nfec A 3 in. B in. C D in. E 3 in. F 1. nmnp > nrqp if NQ intersects MR at point P. N 1 ft P ft R M ft 1 ft Q Chapter Skills Practice 9

28 7 Chapter Skills Practice

29 Lesson. Skills Practice Name Date And Here s Two More! ASA and AAS Congruence Vocabular Define each term in our own words. 1. ASA Congruence Theorem. included side 3. AAS Congruence Theorem Chapter Skills Practice 71

30 Lesson. Skills Practice page Problem Set Determine whether the given triangles in each problem are congruent. 1. Determine whether nabc is congruent to ndef b ASA. B A C D - - m/a 5 m/d 5 5, AC 5 DF 5 5, and m/c 5 m/f 5 9. The triangles are congruent b the ASA Congruence Theorem. F E. Determine whether nghj is congruent to nkmn b ASA. H G J N - - K M 7 Chapter Skills Practice

31 Lesson. Skills Practice page 3 Name Date 3. Determine whether npqr is congruent to nstw b ASA. Q W S P T R Determine whether nabc is congruent to nxyz b ASA. B C Z A Y X Chapter Skills Practice 73

32 Lesson. Skills Practice page 5. Determine whether ndef is congruent to nrst b AAS. E D F T - S - R. Determine whether nadf is congruent to nmtz b AAS. A D F Z - - T M 7 Chapter Skills Practice

33 Lesson. Skills Practice page 5 Name Date 7. Determine whether nbfn is congruent to nchp b AAS. B C F - - N H P. Determine whether nmnp is congruent to ntvw b AAS. P N T M V - - W Chapter Skills Practice 75

34 Lesson. Skills Practice page Determine whether the given triangles in each problem are congruent b ASA or AAS. If there is not enough information to determine whether the triangles are congruent, write not enough information. 9. nabc > nmnp B P 1 in. 5º N A 7º 5º 7º 1 in. C M The triangles are congruent b AAS. 1. ndef > nrst D R 1 ft S º E 1 ft º F T 11. nwxz > nyxz W X 7º 7º 75º 75º Y Z 7 Chapter Skills Practice

35 Lesson. Skills Practice page 7 Name Date 1. nabd > ncbd B A D C 13. njkl > nstw J S T K L W 1. nabd > nfec A B C in. D E F Chapter Skills Practice 77

36 Lesson. Skills Practice page 15. npqt > nsqr if PS intersects RT at point Q. P R Q T S 1. nabc > nedc if BE intersects AD at point C. B D C A E 7 Chapter Skills Practice

37 Lesson. Skills Practice page 9 Name Date 17. nhnk > njpm H 5 cm J 5 cm K 5 cm M N P 1. nqwz > nytp R W T Q Z P Y Chapter Skills Practice 79

38 Chapter Skills Practice

Slide, Flip, Turn: The Latest Dance Craze?

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