For questions 13 16, determine if the described transformation(s) is/are an isometry.

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1 1. What ter describes a transforation that does not change a figure s size or shape? () siilarit () isoetr () collinearit () setr For questions 4, use the diagra showing parallelogra. H I F 6. regular polgon with n sides is carried onto itself b a positive rotation about its center that is a ultiple of 60, but less than 60. Which could NOT be the value of n? () () 4 () 5 () 6 7. In the diagra, g h and lies on line g. 10 c G. reflection across G carries parallelogra onto itself. 5 c () True () False. rotation of 90 about I carries parallelogra onto itself. () True () False 4. rotation of 180 about I carries parallelogra onto itself. () True () False 5. Which of these is equivalent to a translation? () a reflection across one line () a coposition of two reflections across intersecting lines () a coposition of two reflections across parallel lines g h The figure is reflected across line g, and its iage is reflected across line h. What is the distance fro line g to the final iage of point? () 5 c () 15 c () 0 c () 5 c 8. What is the iage of the point ( 4, 6) under the transforation T(, ) (, )? () (6, 4) () ( 6, 4) () (4, 6) () ( 4, 6) age 1 of 47 Revised 11/1/01 lark ount School istrict age of 47 Revised 11/1/01 lark ount School istrict 9. figure is rotated about the origin b 180, then is translated 4 units right and one unit up. Which describes the results of the two transforations? () (, ) ( + 4, + 1) () (, ) ( 4, 1) () (, ) ( + 4, + 1) () (, ) ( 4, + 1) 10. The point (4, ) is rotated 90 about the origin. In which quadrant is '? () I () II () III () IV 11. figure is reflected across the line =, then reflected across the line = 4. Which single transforation results in the sae iage? () a reflection across the line = () a reflection across the line = 6 () a translation units up () a translation 4 units up 1. oint is the iage of point under a transforation T. Line is the perpendicular bisector of at point M. Which describes the transforation T? () a reflection across () a 90 rotation about M () a translation b the vector fro to M () a dilation about M with scale factor For questions 1 16, deterine if the described transforation(s) is/are an isoetr. 1. reflection is an isoetr. () True () False 14. coposition of two reflections is an isoetr. () True () False 15. dilation is an isoetr. () True () False 16. coposition of a rotation and a dilation is an isoetr. () True () False 17. In Δ, M is the idpoint of and N is the idpoint of. For which tpe of triangle is 1 MN =? () equilateral onl () isosceles onl () scalene onl () an triangle age of 47 Revised 11/1/01 lark ount School istrict age 4 of 47 Revised 11/1/01 lark ount School istrict

2 18. Use the diagra. For questions 0, use the diagra where is the reflection of across Q. k 44 Q 0. = () True () False Which series of reflections would result in a rotation of 44 about? () reflect across k then reflect across () reflect across then reflect across k () reflect across then reflect across () reflect across then reflect across 19. fter a figure is rotated, =. Which stateent(s) could be true? 1. Q () True () False. Q = Q () True () False () The center of rotation is. () The angle of rotation is a ultiple of 60. () ither or or both. () Neither nor.. 1 Q= () True () False age 5 of 47 Revised 11/1/01 lark ount School istrict age 6 of 47 Revised 11/1/01 lark ount School istrict For questions 4 6, use the diagra where is a quadrilateral with and. iagonals and intersect at. 7. Use the figure. 4. Δ Δ transforation T is defined as (, ) (, ). Which shows the iage of figure under T? () True () False () () 5. Δ Δ () True () False 6. Δ Δ () True () False () age 7 of 47 Revised 11/1/01 lark ount School istrict age 8 of 47 Revised 11/1/01 lark ount School istrict

3 For questions 8 9, a transforation S is defined as (, ) (, 1). 8. The pre-iage of (, 6) under S is ( 9, 5). () True () False 9. S is an isoetr. () True () False 0. Given point is located at (1, ). What is the final iage of after this series of transforations? (1) Reflect across the ais. () Translate the iage such that (, ) ( 4, + ). () ( 1, ) () (, 5) () (, 1) () ( 5, 5) 1. Which transforation does NOT preserve the orientation of a figure? () dilation () reflection () rotation () translation For questions 5, deterine if the apping is an isoetr.. (, ) (, + ) is an isoetr. () True () False. (, ) (, ) is an isoetr. () True () False 4. (, ) (, ) is an isoetr. () True () False 5. (, ) (, ) is an isoetr. () True () False 6. figure is transfored in the plane such that no point aps to itself. What tpe of transforation ust this be? () dilation () reflection () rotation () translation age 9 of 47 Revised 11/1/01 lark ount School istrict age 10 of 47 Revised 11/1/01 lark ount School istrict For questions 7 8, deterine the truth of the stateents about rotations. 7. Rotations preserve the orientation of a figure. () True () False 8. Under a rotation, no point can ap to itself. () True () False For questions 9 41, point is located at (6, 0) and undergoes a transforation. 9. rotation of 90 about results in =. () True () False 40. translation b the vector 6, 0 results in =. () True () False 41. reflection about the ais results in =. () True () False For questions 4 4, use the diagra which shows Δ has been reflected across an unknown line, then reflected across line to produce Δ The equation of line is = 0.5. () True () False 4. If Δ were reflected across line first, then reflected across line to produce Δ, the equation of line would be = 0.5. () True () False age 11 of 47 Revised 11/1/01 lark ount School istrict age 1 of 47 Revised 11/1/01 lark ount School istrict

4 For questions 44 46, consider a triangle Δ that has been transfored through rigid otions and its iage copared to Δ XYZ. eterine if the given inforation is sufficient to draw the provided conclusion. 47. Look at the figure below. 44. Given onclusion X Y Δ Δ XYZ Z () True () False 45. Given onclusion X Y Δ Δ XYZ YZ () True () False 46. Given onclusion X XY Δ Δ XYZ YZ () True () False Look at these three figures. II I Which figures are congruent to the first figure? () I onl () II onl () I and II onl () I, II, and III 48. Use the diagra. s r 1 4 n III Which stateent would be used to prove lines r and s are parallel? () 1 and are congruent () and 7 are copleentar () 4 and 1 are congruent () 8 and 6 are suppleentar age 1 of 47 Revised 11/1/01 lark ount School istrict age 14 of 47 Revised 11/1/01 lark ount School istrict For questions 49 51, evaluate whether the iage of a figure under the described transforation is congruent to the figure. 49. transforation T follows the rule (, ) ( +, ). The iage of a figure under T is congruent to the figure. () True () False. transforation T follows the rule (, ) (, ). The iage of a figure under T is congruent to the figure. () True () False For questions 5 54, consider Δ where = and = = 140 () True () False 54. = 100 () True () False 55. Use the Venn diagra. 51. transforation T follows the rule (, ) (, ). The iage of a figure under T is congruent to the figure. () True () False Quadrilaterals I II arallelogras Rhobi Squares Rectangles III IV V 5. In the diagra, n and p q. p q Trapezoids VI VII Kites 88 n What is the value of? () 44 () 88 () 9 () 176 quadrilateral has 4 lines of setr. Identif the area of the diagra in which resides. () III () IV () V () VII age 15 of 47 Revised 11/1/01 lark ount School istrict age 16 of 47 Revised 11/1/01 lark ount School istrict

5 56. On the coordinate plane, draw triangles Δ and Δ such that: 60. onstruct an equilateral triangle inscribed in circle O. (1) = () Δ has been rotated In the diagra, is the perpendicular bisector of at, and r ( ) =. O rove Δ Δ. 61. Use the figure. 58. In the diagra, is the perpendicular bisector of. 8 F 8 8 rove. 59. rove the su of the easures of the interior angles of an triangle is (a) Transfor Δ b reflecting it across the -ais to produce Δ. (b) escribe a transforation, or coposition of transforations, that aps Δ to Δ F. (c) escribe a single transforation that aps Δ to Δ F age 17 of 47 Revised 11/1/01 lark ount School istrict age 18 of 47 Revised 11/1/01 lark ount School istrict 6. Ji is building a go-cart to race. Ji sits in a seat toward the left rear corner of the cart. To see other carts behind hi, he ounts plane irrors: one on each side of the cart and one in the center. 6. The diagra shows regular heagon F with center O. F The scale diagra shows a top view of the cart. Front of art O center irror left side irror right side irror For each part, fill in the blank. (a) is the iage of under a 60 rotation about O. (b) The figure is reflected across. The pre-iage of is. (c) F is the iage of when the figure is rotated about O. (d) is first reflected across F. That iage aps to F when reflected across. J Seat 1 foot 64. raw the iage of Δ when reflected across line. (a) Ji s ees are at point J. The irrors are ounted in a wa that Ji does not block his own view. Show the area behind the cart that Ji can see using the irrors. (b) escribe how Ji could iprove his visibilit behind the cart using the sae three irrors age 19 of 47 Revised 11/1/01 lark ount School istrict age 0 of 47 Revised 11/1/01 lark ount School istrict

6 65. raw the iage of Δ when rotated 70 about O. 66. Δ is the iage of Δ when a reflected about line. onstruct line. O ' ' ' age 1 of 47 Revised 11/1/01 lark ount School istrict age of 47 Revised 11/1/01 lark ount School istrict 67. Δ is the iage of Δ when rotated about point O. onstruct point O and copute the angle of rotation. 68. Use scalene right triangle. ' ' escribe and sketch the transforations required so that the union of the triangle and its iage fors (a) a kite. (b) an isosceles triangle. (c) a rectangle. ' age of 47 Revised 11/1/01 lark ount School istrict age 4 of 47 Revised 11/1/01 lark ount School istrict

7 69. Right triangle QR has sides of length 6 units, 8 units, and 10 units. The triangle is dilated b a scale factor of 4 about point Q. What is the area of triangle 'Q'R'? 7. In the diagra, a student has placed a irror on level ground, then stands so that the top of a nearb tree is visible in the irror. () 96 square units () 19 square units () 84 square units () 768 square units 70. In the diagra below H. 8 4 What is the value of? () 1 () 18 () 7 9 H 71. The ratio of the side lengths of a triangle is :6:8. second triangle is siilar to the first and its shortest side easures 8.0 centieters. What is the length of the longest side of the second triangle? ().0 c () 10.7 c () 1.0 c () 1. c What is the height of the tree? () 4 () 5 () 41 () In the diagra, JG QR. Q 7 R J G What is the value of? () 11 () 6 () 5 () age 5 of 47 Revised 11/1/01 lark ount School istrict age 6 of 47 Revised 11/1/01 lark ount School istrict 74. Which figure contains two siilar triangles that are NOT congruent? 77. Use the diagra. () 5 () 5 5 () () 75. Sall constructs a triangle where two of the angles easure and 60. To constructs a triangle where two of the angles easure and 70. What is true about the two triangles? () The triangles cannot be siilar. () The triangles could be siilar. () The triangles ust be siilar. 76. Triangle has vertices (, ), ( 5, 5), and ( 5, ). The triangle is dilated about the point ( 1, 1 ) with scale factor 4. What is the location of '? () ( 8, 8) () ( 10, 10) () ( 11, 5) () ( 14, 6) 5 ilate line about the origin with scale factor. What is the equation of the line s iage? () = + () = + 4 () = 4 + () = Which is NOT a criterion for triangle siilarit? () angle-angle () angle-side-angle () side-angle-side () side-side age 7 of 47 Revised 11/1/01 lark ount School istrict age 8 of 47 Revised 11/1/01 lark ount School istrict

8 79. Use the diagra. 80. In the diagra, segents and intersect at, F lies on, and = 60. F ilate line b a factor 1 about. Which shows the result of the dilation? 60 () ' () The two segents are dilated about F with scale factor 1. What is? ' () 0 () 60 () 90 () 10 () ' () ' age 9 of 47 Revised 11/1/01 lark ount School istrict age 0 of 47 Revised 11/1/01 lark ount School istrict For questions 81 8, use the diagra In the diagra, is dilated with center O to produce '''', and =. G F Let the figure be dilated with scale factor k, where k 0 and k = k ( ). () True () False ' O ' What is O? () 1 ' ' 8. G' is between ' and F'. () True () False 8. = k( ) () 1 () () () True () False age 1 of 47 Revised 11/1/01 lark ount School istrict age of 47 Revised 11/1/01 lark ount School istrict

9 85. Use the figure below. 87. J (5, 7) is the iage of J(, ) after a dilation with scale factor. Where is the center of dilation? () (, 9) () (0, 0) () (, 1) () (4, 5) 88. Fred stands at corner of a rectangular field shown below. He needs to get to corner. Which shows the figure dilated about the origin with scale factor 1.5? () () 9 1 What is the shortest distance fro to? () () 9 () 1 () 15 () Use the right triangle. What is the value of? One verte of a polgon is ( 4, 5). If the polgon is dilated about the point (0, ) with scale factor, what is the location of? () ( 8, 8) () ( 8, 10) () (8, 10) () (8, 4) What is the value of? () 7 () 161 () 7 () age of 47 Revised 11/1/01 lark ount School istrict age 4 of 47 Revised 11/1/01 lark ount School istrict 90. Use the diagra. 9. In the diagra, Δ is a dilation of Δ. b h a ' c ' ' Which is equal to h? () a (a) Find the center of dilation O. (b) opute the scale factor of the dilation. () b () () ab 91. Use the diagra. 9. rove that an two isosceles right triangles are siilar. 94. In the diagra, Δ is a right triangle with right angle, and is an altitude of Δ. b a F d c e Use the fact that Δ Δ Δ to prove a + b = c. 95. Triangle One has vertices (, 4), (, 8), and (5, 4). Triangle Two is siilar to Triangle One and has two of its vertices at ( 1, 1) and ( 7, 1). Given: rove: Δ Δ (a) raw Triangle One and Triangle Two on the coordinate plane and label the vertices. (b) raw and label a third triangle that is siilar to Triangle One, has two vertices at ( 1, 1) and ( 7, 1), but is not congruent to Triangle Two age 5 of 47 Revised 11/1/01 lark ount School istrict age 6 of 47 Revised 11/1/01 lark ount School istrict

10 96. Triangle has sides of length, 6, and 8. Triangle F is siilar to triangle and has one side with length 4. (a) What are the possible scale factors of the dilation of triangle to triangle F? (b) opute one possible area of triangle F. 99. sall airplane flies due north at 1 kiloeters per hour. wind is blowing towards the direction 60 east of north at kiloeters per hour. Which figure represents the final speed and direction of the airplane? N N N N () 00 () 00 () 00 () The diagra shows a surveor s ap Use the diagra The surveor is tring to easure the direct distance between points and, which are on opposite sides of a lake. Fro point, point is 9 eters awa in a direction 0 west of north. Fro point, point is 880 eters awa in a direction east of north. Which represents the distance between and? () ( 9)( 880) cos () + sin sin 0 9 sin 70 () sin onsider a triangle. Which stateent is true? () c = a b abcos () c = a b + abcos () c = a + b abcos () c = a + b + abcos What is cos? () () () () age 7 of 47 Revised 11/1/01 lark ount School istrict age 8 of 47 Revised 11/1/01 lark ount School istrict For questions , consider a triangle and each given set of easureents. 101.,, and are sufficient to solve the triangle using the Law of Sines. () True () False 105. In the diagra, Δ is a non-right triangle. a b 10.,, and are sufficient to solve the triangle using the Law of Sines. () True () False 10.,, and are sufficient to solve the triangle using the Law of Sines. () True () False 104. The diagra shows a parallelogra. Which describes the area of the triangle? () 1 ab () absin () 1 sin ab () 1 cos ab c 106. Given: cos and sin What is the approiate value of cos 154? 5 60 () 0.90 () 0.44 () 0.44 () 0.90 What is the parallelogra s area? () 7.5 () 15 () 15 () age 9 of 47 Revised 11/1/01 lark ount School istrict age 40 of 47 Revised 11/1/01 lark ount School istrict

11 For questions use the stateent below. Given: n angle easures k, where k > In Δ where is a right angle, sin =. What is cos? sin k = cos( 90 k) () True () False () () sin k = sin( 180 k) () 4 () True () False () cos k = cos( 180 k) () True () False 11. Use the diagra Let cos =. What is the value of sin? () () 1 () 1 () 1 1 Which stateent is true? 1 () sin = 5 1 () cos = 1 1 () tan = age 41 of 47 Revised 11/1/01 lark ount School istrict age 4 of 47 Revised 11/1/01 lark ount School istrict 11. Use the diagra. For questions , let cos = cos( 180 ) = Which is the value of? () = 41cos5 tan5 () = () = cos5 41 () = tan Use the diagra. 5 5 d 45 What is the value of d? () 5 () 5 () 10 () () True () False 116. cos( 90 ) = () True () False 117. sin ( 90 ) = () True () False 118. Let a = cos 8. Which stateent is true? () a = cos 6 () a = cos 15 () a = sin 6 () a = sin What is cos? () 0 () 45 () 60 () age 4 of 47 Revised 11/1/01 lark ount School istrict age 44 of 47 Revised 11/1/01 lark ount School istrict

12 10. In the diagra, < and =. 1. In Δ GHI, the sine of angle G equals 1. Δ GHI is a dilation of Δ GHI about G with a scale factor of. What is the sine of angle G'? () 1 4 Which stateent is true? () cos < sin () cos = sin () cos > sin 11. What is tan 60? () () () 1 () 1 1. What is tan () 1? () 0 () 45 () 60 () 90 () 1 () () In triangle Δ, = 5, a = 6., and b = 4. Find all possible easures of the reaining two angles and the third side. 15. In triangle Δ, = 5, a = 6., and c = 4. (a) Find all possible easures of the reaining two angles and the third side. (b) Find all possible areas of the triangle age 45 of 47 Revised 11/1/01 lark ount School istrict age 46 of 47 Revised 11/1/01 lark ount School istrict 16. The diagra shows a odel of a closet floor on which Ki is laing carpet. (Measureents are approiate.) (a) What is the area of the closet? (b) The carpet Ki is using is cut b the carpet store in rectangular pieces fro a 4-foot wide roll. What is the shortest length of carpet Ki would need to cover the closet floor in a single piece? Justif our answer age 47 of 47 Revised 11/1/01 lark ount School istrict