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Transcript

Name: _________________________________________________ Geometry Regents Review In this packet you will find all of your regents review questions to be completed as assigned. The due date for each regents assignment is listed below. They should be completed and handed in on the day stated. If you are absent they should be handed in the next day. Each question is worth 2 points. All work and answers should be completed on the answer sheets provided. You must show work or provide an explanation for all problems (EVEN MULTIPLE CHOICE) or you will receive no credit for the solution. An explanation can include showing a drawing, stating a definition used, or showing a formula. Each assignment will be graded as a quiz worth 20 points. An unexcused late assignment will lose 5 points for each day it is late. If you hand in all of the assignments for the quarter, then I will drop your lowest of the quiz grades. You may come to extra help for any of the problems at any time, and you are allowed to hand assignments in early. Assignment Number Due Date Questions #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 March 11 March 18 March 25 April 1 April 8 April 23 April 29 May 6 May 20 May 27 1-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100 1. A line segment has endpoints 2. What is the image of the point and . What are the coordinates of the midpoint of under the translation ? ? 3. When writing a geometric proof, which angle relationship could be used alone to justify that two angles are congruent? 1) supplementary angles 3) adjacent angles 2) linear pair of angles 4) vertical angles 4. The vertices of the triangle in the diagram below are What are the coordinates of the centroid of 1) 2) , , and . ? 3) 4) 5. Which set of numbers does not represent the sides of a right triangle? 1) 3) 2) 4) 6. What is an equation of the line that passes through the point and is parallel to the line whose equation is ? 1) 3) 2) 4) 7. In scalene triangle ABC, shortest? and . What is the order of the sides in length, from longest to 8. Which compound statement is true? 1) A triangle has three sides and a quadrilateral has five sides. 2) A triangle has three sides if and only if a quadrilateral has five sides. 3) If a triangle has three sides, then a quadrilateral has five sides. 4) A triangle has three sides or a quadrilateral has five sides. 9. The two lines represented by the equations below are graphed on a coordinate plane. Which statement best describes the two lines? 1) The lines are parallel. 2) The lines are the same line. 3) The lines are perpendicular. 4) The lines intersect at an angle other than 90°. 10. In circle O, a diameter has endpoints 1) 2) and . What is the length of the diameter? 3) 4) 11. The point is rotated 90º about the origin and then dilated by a scale factor of 4. What are the coordinates of the resulting image? 1) 3) 2) (12,-8) 4) 12. In the diagram below of . What is 13. In the diagram below of isosceles triangle with , side is extended to point D, , , and ? , B is a point on . Find . 14. Triangle ABC has vertices , image of after the transformation , and . such that is an equilateral triangle, and . Find the coordinates of the vertices of 15. Find, in degrees, the measures of both an interior angle and an exterior angle of a regular pentagon. 16. Find the slope of a line perpendicular to the line whose equation is . is an , the 17. Line n intersects lines l and m, forming the angles shown in the diagram below. Which value of x would prove 1) 2.5 2) 4.5 18. A line segment has endpoints 19. In , ? 3) 6.25 4) 8.75 and . What is the length of the segment? and an exterior angle at vertex H has a measure of 104. What is 20. The angles of triangle ABC are in the ratio of ? . What is the measure of the smallest angle? 21. Which statement is the negation of “Two is a prime number” and what is the truth value of the negation? 1) Two is not a prime number; false 3) A prime number is two; false 2) Two is not a prime number; true 4) A prime number is two; true 22. The diagram below shows a pair of congruent triangles, with Which statement must be true? 1) 2) and 3) 4) 23. What is an equation of the line that is perpendicular to the line whose equation is through the point 24. In 1) 2) 3) 4) , ? and . . Which inequality is true? and that passes 25. The number of degrees in the sum of the interior angles of a pentagon is 1) 72 3) 540 2) 360 4) 720 26. What is the equation of a line passing through ? 27. The coordinates of the endpoints of is 1) 2) are and parallel to the line represented by the equation and 3) 4) 28. In the diagram below, point P is the centroid of If 1) 9 2) 2 29. In feet? 1) 2) 30. If 1) 2) and . The equation of the perpendicular bisector of , what is the length of . ? 3) 18 4) 27 , feet and feet. Which inequality represents all possible values for the length of , in 3) 4) and is the shortest side of 31. As shown in the diagram below, Which statement is always true? 1) 2) is a median of , what is the shortest side of 3) 4) ? . 3) 4) 32. Line segment AB is a diameter of circle O whose center has coordinates B if the coordinates of point A are ? 1) 3) 2) 4) . What are the coordinates of point 33. What is the slope of the line perpendicular to the line represented by the equation 34. Square ABCD has vertices , , 35. The diagram below shows , with , , and ? . What is the length of a side of the square? , and . If , what is 36. Which set of numbers could not represent the lengths of the sides of a right triangle? 1) 3) 4) 2) 37. The equation of a line is that passes through the point . What is an equation of the line that is perpendicular to the given line and ? 38. Consider the relationship between the two statements below. These statements are 1) inverses 2) Converses 39. In the diagram of trapezoid ABCD below, ? 3) contrapositives 4) biconditionals , , 40. Which equation represents a line that is parallel to the line whose equation is 1) 3) 2) , and . What is ? 4) 41. The measure of an interior angle of a regular polygon is 120°. How many sides does the polygon have? 1) 5 3) 3 2) 6 4) 4 ? 42. As shown in the diagram of rectangle ABCD below, diagonals If 1) 6 2) 10 and 43. If the vertices of 1) right 2) scalene , then the length of and intersect at E. is 3) 12 4) 24 are , , and , then is classified as 3) isosceles 4) equilateral 44. Write an equation of the line that is the perpendicular bisector of the line segment having endpoints . [The use of the grid below is optional] 45. Triangle ABC has vertices , the image of below is optional.] and , and . State and label the coordinates of the vertices of , following the composite transformation . [The use of the set of axes 46. In the diagram below of rhombus ABCD, 47. In the diagram of quadrilateral ABCD, Which method can be used to prove 1) AAS 2) SSA . What is , is congruent to 48. In the diagram below, MATH is a rhombus with diagonals If 1) 12 2) 78 , what is ? , and diagonal is drawn. ? 3) SAS 4) SSS and . ? 3) 84 4) 156 49. Triangle ABC is similar to triangle DEF. The lengths of the sides of the shortest side of if its perimeter is 60? 1) 10 3) 20 2) 12.5 4) 27.5 are 5, 8, and 11. What is the length of 50. Juliann plans on drawing , where the measure of can range from 50° to 60° and the measure of can range from 90° to 100°. Given these conditions, what is the correct range of measures possible for ? 1) 20° to 40° 3) 80° to 90° 2) 30° to 50° 4) 120° to 130° 51. In the diagram of and below, Which method can be used to prove 1) SSS 2) SAS 52. Point A is located at 1) 2) , , and ? 3) ASA 4) HL . The point is reflected in the x-axis. Its image is located at 3) 4) 53. What is an equation of the line that passes through the point is . and is perpendicular to the line whose equation ? 54. In an equilateral triangle, what is the difference between the sum of the exterior angles and the sum of the interior angles? 55. In , this triangle? 1) 2) , , and . Which expression correctly relates the lengths of the sides of 3) 4) 56. What is the contrapositive of the statement, “If I am tall, then I will bump my head”? 1) If I bump my head, then I am tall. 2) If I do not bump my head, then I am tall. 3) If I am tall, then I will not bump my head. 4) If I do not bump my head, then I am not tall. 57. In the diagram of found it to be 6 inches. If 1) 2) 3) 4) below, Jose found centroid P by constructing the three medians. He measured , which equation can be used to find x? and 58. In the diagram below, the length of the legs Altitude is drawn to the hypotenuse of 59. In the diagram of and and of right triangle ABC are 6 cm and 8 cm, respectively. . What is the length of to the nearest tenth of a centimeter? below, Which method can be used to show that 1) SAS 2) AA and intersect at C, and must be similar to 3) SSS 4) HL . ? 60. Which equation represents a line perpendicular to the line whose equation is 1) 3) 2) 4) 61. In , point D is on the length of , and point E is on such that . If ? , , and , what is ? 62. In the diagram of below, connecting the midpoints of the sides of , , and . Find the perimeter of the triangle formed by . 63. Find an equation of the line passing through the point and parallel to the line whose equation is 64. Given: Two is an even integer or three is an even integer. Determine the truth value of this disjunction. Justify your answer. . 65. In the diagram below, , , and . Determine the value of x. 66. In the diagram below of right triangle ABC, altitude is drawn to hypotenuse what is the length of altitude in simplest radical form? . If 67. What is the negation of the statement “I am not going to eat ice cream”? 68. In isosceles triangle ABC, 1) 2) . Which statement will always be true? 3) 4) 69. The rectangle ABCD shown in the diagram below will be reflected across the x-axis. What will not be preserved? 1) slope of 2) parallelism of and 3) length of 4) measure of and , 70. If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral could be a 1) rectangle 3) square 2) rhombus 4) trapezoid 71. What is the converse of the statement "If Bob does his homework, then George gets candy"? 72. In 1) 2) , , , and 73. In isosceles trapezoid ABCD, the trapezoid? . Which statement about the angles of 3) 4) . If , , and must be true? , what is the length of the altitude of 74. What is the length, to the nearest tenth, of the line segment joining the points and 75. What is the slope of a line perpendicular to the line whose equation is ? ? 76. The diagram below shows a pennant in the shape of an isosceles triangle. The equal sides each measure 13, the altitude is , and the base is 2x. What is the length of the base? 1) 5 2) 10 3) 12 4) 24 77. Two lines are represented by the equations and parallel? 1) 2) . For which value of m will the lines be 3) 3 4) 12 78. The coordinates of the vertices of parallelogram ABCD are , , of which line segments could be calculated to show that ABCD is a rectangle? 1) 3) and and 2) 4) and and 79. In the diagram below of , . Find the perimeter of is a midsegment of . , , , and , and . The slopes 80. Triangle XYZ, shown in the diagram below, is reflected over the line of , the image of . 81. In the diagram below of , medians , , and 12 cm. What is the length, in centimeters, of ? . State the coordinates intersect at G. The length of is 82. In the diagram below, line p intersects line m and line n. If 1) 12.5 2) 15 and , lines m and n are parallel when x equals 3) 87.5 4) 105 83. What is the length of the line segment whose endpoints are 84. The equation of line k is 1) 2) 3) 4) . The equation of line m is parallel perpendicular the same line neither parallel nor perpendicular and ? . Lines k and m are 85. In the diagram of is the measure of below, 86. Triangle ABC has vertices 1) equilateral 2) isosceles 3) right 4) scalene , 87. In rhombus ABCD, the diagonals length of ? 88. In 1) 2) 3) 4) , , , and is extended through N. What ? , 89. As shown in the diagram below, What is the length of ? , and and . The triangle may be classified as intersect at E. If , and and , what is the . Which statement is true? , 90. Which line is parallel to the line whose equation is ? 1) 3) 2) 4) , , , and . and also passes through the point 91. If the vertex angles of two isosceles triangles are congruent, then the triangles must be 1) acute 3) right 2) congruent 4) similar 92. Which quadrilateral has diagonals that always bisect its angles and also bisect each other? 1) rhombus 3) parallelogram 2) rectangle 4) isosceles trapezoid 93. What is the slope of a line that is perpendicular to the line whose equation is 94. In the diagram below of right triangle ABC, altitude is drawn to hypotenuse and . What is the length of in simplest radical form? ? , , 95. Given the true statement, "The medians of a triangle are concurrent," write the negation of the statement and give the truth value for the negation. 96. A pentagon is drawn on the set of axes below. If the pentagon is reflected over the y-axis, determine if this transformation is an isometry. Justify your answer. [The use of the set of axes is optional.] 97. In the diagram below of inches, inches, and . , D is a point on , E is a point on , , inches. Find, to the nearest tenth of an inch, the length of 98. In the diagram of ? below, . The measure of 99. In the diagram below of parallelogram ABCD with diagonals . What is the measure of 1) 15º 2) 30º 3) 45º 4) 60º is 40°. What is the measure of and , and ? 100. On the set of axes below, Geoff drew rectangle ABCD. He will transform the rectangle by using the translation and then will reflect the translated rectangle over the x-axis. What will be the area of the rectangle after these transformations? 1) exactly 28 square units 2) less than 28 square units 3) greater than 28 square units 4) It cannot be determined from the information given.