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GeometryRegularSemester1Review 2015โ2016 1. Any triangle may be rotated and translated so that one vertex is at the origin and another vertex is on the positive x-axis. What is the relationship between the length of ๐ท๐ธ one of the triangle's midlines, and the length of ๐ต๐ถ? 3. If โ ๐ด๐ธ๐ต = 2๐ฅ + 32 and โ ๐ท๐ธ๐ถ = ! ๐ฅ + 65 what is the value of ๐ฅ? ! A. โ22 B. 19.5 C. 22 D. 58 4. ! A. ๐ท๐ธ = ! ๐ด๐ถ B. !" !" !" = !" ! If line r and s are parallel, then all of the following statements are valid conclusions except: C. ๐ท๐ธ = ! ๐ต๐ถ ! D. ๐ท๐ธ = ! ๐ด๐ต A. โ 3 โ โ 7 B. โ 1 โ โ 5 C. โ 1 โ โ 7 D. โ 3 โ โ 6 2. Find the length of ๐ป๐ผ. 8x+5 H A. 4 C. 19 2x+10 I B. 18 D. 37 3x+7 J 5. Point A has the coordinates (2, 5). Point B has the coordinates (6, 17). How long is segment ๐จ๐ฉ in simplified radical form? A. 160 C. 16 10 B. 48 D. 4 10 Fall2015 GeometryRegularSemester1Review 2015โ2016 6. Select all undefined terms from the below list. I. Point IV. Plane II. Ray V. Line III. Segment VI. Angle A. B. C. D. 9. Raymond threw a ball that bounced up at an angle of (2x +4). What is the value of x? I, II, IV, V I, II, V I, IV, V I, III, IV, V 7. Marcy made the following statement: โIf two lines are parallel, then they have the same slope.โ Which of the following is a correct analysis of Marcyโs statement? A. Marcyโs statement is true. B. Marcyโs statement is false. The slopes of the lines are negative reciprocals. C. Marcyโs statement is sometimes true. D. Marcyโs statement is false, but the converse is true. 3x+6 2x+4 A. 16 B. 36 C. 45 D. 54 10. ๐ด๐ต โฅ ๐ถ๐ท Find ๐โ ๐ด๐ต๐ถ B 10x-30 A 8. Find the contrapositive of the following statement: โIf Jack plays baseball, then Jack participates in sports.โ A. If Jack participates in sports, then Jack plays baseball. B. If Jack does not play baseball, then Jack does not participate in sports. C. If Jack does not play baseball, then Jack participates in sports D. If Jack does not participate in sports, then Jack does not play baseball. D 5x+5 C A. 7 B. 40 C. 140 D. 180 Fall2015 GeometryRegularSemester1Review 2015โ2016 11. Which graph best represents a line parallel to the line with the equation ๐ฆ = โ3๐ฅ โ 2 ? 12. A line passes through point (6, โ3) ! with a slope of !. Write the equation of the line in slopeintercept form. ! A. ๐ฆ = โ ! ๐ฅ โ 7 ! B. ๐ฆ = โ ! ๐ฅ + 7 ! C. ๐ฆ = ! ๐ฅ + 7 ! D. ๐ฆ = ! ๐ฅ โ 7 A. 13. ๐ท๐ธ๐น๐บ is translated 6 units to the right and 4 units up. What are its new coordinates? B. C. D. A. ๐ (โ3, โ1), ๐(0, โ1), ๐ (0, โ4), ๐(โ3, โ4) B. ๐ (โ6,1), ๐(โ3,1), ๐ (โ3, โ2), ๐(โ6, โ2) C. ๐ (0,1), ๐(3,1), ๐ (3, โ2), ๐(0, โ2) D. ๐ (0, โ3), ๐(3, โ3), ๐ (3, โ6), ๐(0, โ6) 14. Classify the triangle with vertices at the following coordinates R(โ2, โ2), S(1, 4), T(4, โ5). A. Scalene B. Isosceles C. Equilateral D. Not enough Information Fall2015 GeometryRegularSemester1Review 2015โ2016 15. The Missing statements are listed below, but they are out of order. Statement R: โ๐๐๐ โ โ๐๐๐ (Angle-Side-Angle โ ) Statement S: โ ๐ โ โ 4 (Alternate Interior Angles) Statement T: ๐ณ๐ต โ ๐ธ๐ต (Corresponding Parts of โ โโฒ๐ ) What is the correct order for these statements to be placed in the proof above? A. Statement S, Statement T, Statement R B. Statement R, Statement S, Statement T C. Statement R, Statement T, Statement S D. Statement S, Statement R, Statement T Fall2015 GeometryRegularSemester1Review 2015โ2016 16. 18. Based on the drawing, which of the following rules could be used to prove โ UVWโ โ๐๐๐? To show โ ๐๐๐ โ โ ๐๐๐ using Corresponding Parts of Congruent Triangles are Congruent, which of the following would you need to prove? A. โ ๐ถ๐๐ โ โ ๐ต๐ธ๐ท B. ๐๐ โ ๐ธ๐ท C. โ ๐ท๐ต๐ธ โ โ ๐๐ถ๐ D. โ๐ถ๐๐ โ โ๐ต๐ธ๐ท A. HypotenuseโLeg B. Side-Angle-Side C. Angle-Side-Angle D. Side-Side-Side 19. 17. Which set of given information does not prove โ๐ถ๐ด๐ โ โ๐ถ๐๐? โ๐จ๐ฉ๐ช is isosceles, where ๐จ๐ฉ โ ๐ฉ๐ช. A. โ MCA โ โ ๐๐ถ๐, โ CAM โ โ COM If ๐โ ๐ด = 5๐ฅ + 30 and ๐ โ ๐ต = 2๐ฅ, then find ๐โ ๐ถ. B. ๐ด๐ถ โ ๐๐ถ, โ ACM โ โ OCM C. ๐ด๐ถ โ ๐๐ถ, โ CAM โ โ ๐ถ๐๐ A. 180° B. 80° C. 20° D. 10° D. ๐ถ๐ด โ ๐ถ๐, ๐ด๐ โ ๐๐ Fall2015 GeometryRegularSemester1Review 2015โ2016 20. What are the coordinates of the image of the point (โ4, 12) under a dilation with a scale factor of 4 and the center of dilation at the origin? A. (โ1, 3) B. (โ16, 12) C. (โ16, 48) D. (8, 48) 21. What is the measure of โ ๐ in the figure shown here? 24. B 4 5 A 6 C 4 List the angles in order from smallest to largest. A. โ ๐ด, โ ๐ต, โ ๐ถ B. โ ๐ต, โ ๐ถ, โ ๐ด C. โ ๐ถ, โ ๐ด, โ ๐ต D. Not enough information 25. Each side of a square is 80 units. Find the length of the squaresโ diagonal. A. B. C. D. 33° 48° 57° 66° 22. To locate the _________________ of a triangle, you can construct the medians of each side of the triangle. A. Centroid B. Circumcenter C. Circumcircle D. Incenter A. 80 B. 40 C. 80 2 D. 40 2 23. To locate the _________ of a triangle, you can construct the perpendicular bisector of each side of the triangle. A. Circumcenter B. Incenter C. Median D. Circumcircle Fall2015 GeometryRegularSemester1Review 2015โ2016 26. In โ๐ท๐ธ๐น, DE = 7 cm and EF = 12 cm. Which of the following could be a possible length of DF? 28. Figure ABCD is a kite. A E 7 cm D A. B. C. D. 93° 12 cm D F 5 cm 10 cm 19 cm 24 cm B 100° C Find ๐โ ๐ถ. A. 32° B. 67° C. 93° D. 100° 27. 29. Each of the following statements about similar pentagons DEFGH and JKLMN is true except: E 11 13 D F What is the classification of the triangle? A. Acute B. Right C. Obtuse D. Not enough information A. The ratio of the corresponding sides of pentagons DEFGH and JKLMN is 2:1. B. Pentagon DEFGH I twice as big as pentagon JKLMN. C. Both pentagons have corresponding angles that are congruent. D. Pentagon JKLMN is the result of a translation of pentagon DEFGH. Fall2015 GeometryRegularSemester1Review 2015โ2016 30. The two trapezoids in the figure are similar, with ๐จ๐ฉ๐ช๐ซ~๐ณ๐ด๐ฑ๐ฒ. If the lengths of sides ๐ต๐ถ, ๐ถ๐ท, and ๐ฝ๐ and are known, then what is the other side length that can be determined using a proportion? 32. Desiree is designing two flowerbeds for her backyard. The flowerbeds are to be similar rectangles. The length of the larger bed will be 8ft and the length of the smaller bed will be 4 ft. Desiree wants the width of the larger bed to be 5ft. For the flowerbeds to be similar, what should be the width of the smaller bed? A. B. C. D. A. AB C. KL ๐ค ๐ค ๐ค ๐ค = = = = 2.5ft 5ft 10ft 13ft B. JK D. ML 33. 31. The two trapezoids in the figure are similar, with ๐จ๐ฉ๐ช๐ซ ~ ๐ณ๐ด๐ฑ๐ฒ. If ๐จ๐ฉ = ๐๐, ๐จ๐ซ = ๐๐, ๐ช๐ซ = ๐ and ๐ณ๐ฒ = ๐๐ what is LM? An equilateral triangle is contained within the isosceles trapezoid shown above. What is the measurement of the largest angle within this diagram (ignoring the straight angle)? A. B. C. D. 12 15 21.6 27 A. B. C. D. 120° 110° 100° 60° Fall2015 GeometryRegularSemester1Review 2015โ2016 34. What is the missing property of equality for the algebraic proof? Statements Reasons 1. 4๐ฅ โ 7 = 2๐ฅ + 3 1. Given equation 2. 2๐ฅ โ 7 = 3 2. Subtraction Property 3. 2๐ฅ = 10 3. ________________________ 4. ๐ฅ = 5 4. Division Property A. Addition Property B. Multiplication Property C. Reflexive Property D. Substitution Property 35. Triangle PQR has vertices at ๐ท โ3, 3 , ๐ธ โ3, โ2 and ๐น โ1, โ2 . This triangle is transformed to make โ๐ ! ๐! ๐! , as shown. 36. Rectangle ๐น๐ช๐ป๐ฎ has two of its vertices at ๐น(โ2,3) and ๐ช(โ2, โ1). Which of the following could be the coordinates for the other two vertices of this rectangle? A. ๐ (5, 2) and ๐บ (5, 6) B. ๐ (โ2, 4) and ๐บ (โ2, 8) C. ๐ (5, โ1) and ๐บ (5, 3) D. ๐ (โ2, โ3) and ๐บ (โ2, 7) 37. What is ๐โ ๐ท? A. 30 B. 60 C. 90 D. 120 If this transformation is a reflection, then what are the coordinates for point R'? A. 1, โ2 B. 1, 3 C. (5, โ2) D. (5, 3) Fall2015 GeometryRegularSemester1Review 2015โ2016 38. Quadrilateral ABCD has vertices at ๐จ(2,6), ๐ฉ(4,2), ๐ช(6,4) and ๐ซ(5,6). The x- and y-coordinates of each of these points are multiplied by โ1.5 to create a similar quadrilateral in Quadrant III. 39. In Geometry class, students are using parallelograms that have been cut out of construction paper. Using one of these paper shapes, a student tears two consecutive corners from a parallelogram. Which similarity statement best describes the relationship between these two figures? Which best describes the relationship between these two corners that have been removed from the parallelogram? A. B. C. D. ABCD~MGRT ABCD~TRGM ABCD~GRTM ABCD~GMTR A. B. C. D. Fall2015 GeometryRegularSemester1Review 2015โ2016 40. In triangle ABC, ๐โ ๐ด = ๐ฅ โ 30 °, ๐โ ๐ต = 2๐ฅ โ 80 °, and ๐โ ๐ถ = ๐ฅ โ 70 °. What kind of triangle is โABC? A. B. C. D. Acute scalene Equilateral Obtuse scalene Right scalene 43. What is the value of x? 10 cm 13 cm x cm A. B. C. D. 41. 7 3 23 16 44. What is the midpoint of A(โ2, 5) and B(7, โ3)? A. B. C. D. In โABC, M and N are midpoints of sides. Which statement best describes the relationship between MN and AC in โABC? 45. If M is the midpoint of ๐ฟ๐ for L(โ3, 4) and M(1, โ2), what are the coordinates of N? A. B. C. D. ! A. MN = ! AC B. AC = 2MN C. MN โฅ AC D. All of the above 42. What is the value of x? (4.5, 1) (2.5, 1) (2.5, 4) (5, 2) (โ1, 1) (5, โ8) (4, โ6) (โ2, 2) 46. How many lines of symmetry in the regular polygon below? (3x)° (2x โ 5)° A. B. C. D. 30 20 5 37 (4x + 25)° A. 2 C. 6 B. 3 D. 12 Fall2015 GeometryRegularSemester1Review 2015โ2016 47. Choose from the below reasons to complete the proof. 48. Which value of x makes โ! โฅ โ! ? A. Linear Pair Theorem B. Addition Property C. Subtraction Property D. Definition of supplementary E. Reflexive Property F. Substitution Property G. Triangle Sum Theorem H. Symmetric Property (4x โ 5)° (5x + 5)° โ! โ! โ! A. B. C. D. 5 30 10 20 Given: โ 1, โ 2 and โ 3 are interior angles of a triangle and exterior angle โ 4 1 Prove: ๐โ 1 + ๐โ 2 = ๐โ 4 2 Statements 1. ๐โ 1 + ๐โ 2 + ๐โ 3 = 180° Reasons 1. 2. โ 3 ๐๐๐ โ 4 are supplementary 2. 3. ๐โ 3 + ๐โ 4 = 180° 3. 4. ๐โ 1 + ๐โ 2 + ๐โ 3 = ๐โ 3 + ๐โ 4 4. 5. ๐โ 1 + ๐โ 2 = ๐โ 4 5. 3 4 49. Determine which if the below statements are true. I. II. III. IV. A. B. C. D. All squares are rhombi. All parallelograms are rectangles. All kites are quadrilaterals. All trapezoids are parallelograms. I only I and II I and III II and IV 50. Which type of transformation does NOT result in a rigid motion? A. B. C. D. Dilation Reflection Rotation Translation Fall2015 GeometryRegularSemester1Review 2015โ2016 51. What is the value of x in the trapezoid? 54. Which property justifies that ๐๐ โ ๐๐ ? Q 105° R P x° A. B. C. D. S 105 75 180 85 A. B. C. D. 52. Given ๐โ ๐๐๐ = 120°, what is ๐โ ๐๐๐ ? Transitive Symmetric Reflexive Reflective 55. Which of the following lengths of triangles can be classified as obtuse? S P (9x + 5)° Q A. B. C. D. R (2x + 5)° 10 25 90 95 A. B. C. D. 8 cm, 15 cm, 17 cm 9 cm, 12 cm, 14 cm 13 cm, 14 cm, 18 cm 15 cm, 20 cm, 26 cm 56. How many distinct line segments exist in the figure below? 53. Quadrilateral ABCD is formed with A(1, 2), B(3, 5), C(6, 3), and D(3, 0). Which could be used to prove that โ ๐ด๐ต๐ถ is a right angle? ! A. The slope of ๐ด๐ต is !, and the slope ! of ๐ต๐ถ is !. They are equal. ! B. The slope of ๐ด๐ต is !, and the slope ! of ๐ต๐ถ is โ !. They are opposite reciprocals. ! C. The slope of ๐ด๐ต is !, and the slope ! of ๐ต๐ถ is โ !. They are opposite reciprocals. D. Not enough information. V W A. 4 B. 5 X Y Z C. 10 D. 16 57. What is the slope of the line parallel to the line given by the below equation? 3๐ฅ โ 2๐ฆ = 12 A. 2 3 B. 3 2 C. โ 2 3 D. โ 3 2 Fall2015 GeometryRegularSemester1Review 2015โ2016 58. What is the slope of the line perpendicular to the line given by the below equation? 3๐ฅ โ 2๐ฆ = 12 A. 2 3 B. 3 2 C. โ 2 a c g 59. Angles a and d are NOT ________________. a b d c adjacent supplementary complementary a linear pair b d A. B. C. D. complementary supplementary adjacent vertical h 61. Angles a & h : A. Corresponding B. Same-side interior C. Alternate interior D. Alternate exterior 62. Angles a & e : A. Corresponding B. Same-side interior C. Alternate interior D. Alternate exterior 60. Angles b and d are ________________. a b d f e 3 D. โ 3 2 A. B. C. D. For 61-64, use the diagram below to identify the relationship between the angles. c 63. Angles d & f : A. Corresponding B. Same-side interior C. Alternate interior D. Alternate exterior 64. Angles c & f : A. Corresponding B. Same-side interior C. Alternate interior D. Alternate exterior Fall2015 GeometryRegularSemester1Review 2015โ2016 65. Write the converse of the following statement and give its truth value. โIf a number is divisible by 6, then it is divisible by 2.โ 69. JKLN is a square. M is the midpoint of ๐๐ฟ. Justify why โ๐ฝ๐๐ โ โ๐พ๐ฟ๐. A. If a number is not divisible by 6, then it is not divisible by 2. True. B. If a number is divisible by 2, then it is divisible by 6. False. C. If a number is not divisible by 6, then it is not divisible by 2. False. D. If a number is divisible by 2, then it is divisible by 6. True. 66. Felicia wants to install an island in her kitchen. She wants to position the island so that it is equidistant from the vertices of a triangle formed by the sink, the refrigerator, and the stovetop. Which point of concurrency should be used to position the island? A. B. C. D. K J N A. B. C. D. M L SSS SAS AAS HL Centroid Incenter Circumcenter Median 67. Which point of concurrency is equidistant to the sides of a triangle? A. B. C. D. Centroid Incenter Circumcenter Median 68. Which point of concurrency is the center of gravity of a triangle? A. B. C. D. Centroid Incenter Circumcenter Median Fall2015