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Transcript

1. What is the slope of a line perpendicular to the line whose equation is 1) ? 2) 3) 4) 2. What is the equation of a line passing through equation ? 1) and parallel to the line represented by the 2) 3) 4) 3. A line segment has endpoints ? 1) 2) and . What are the coordinates of the midpoint of 3) 4) 4. Point M is the midpoint of . If the coordinates of A are , what are the coordinates of B? 1) 2) 3) 4) and the coordinates of M are 5. Find, in simplest radical form, the length of the line segment with endpoints whose coordinates are and . 6. Which illustration shows the correct construction of an angle bisector? 1) 3) 2) 4) 7. Which diagram shows the construction of the perpendicular bisector of 1) 2) 3) 4) ? 8. Which geometric principle is used to justify the construction below? 1) A line perpendicular to one of two parallel lines is perpendicular to the other. 2) Two lines are perpendicular if they intersect to form congruent adjacent angles. 3) When two lines are intersected by a transversal and alternate interior angles are congruent, the lines are parallel. 4) When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel. 9. Which diagram shows the construction of an equilateral triangle? 1) 2) 3) 4) 10. In 1) 2) 3) 4) , right scalene isosceles equilateral , , and . Which type of triangle is ? 11. Tina wants to sew a piece of fabric into a scarf in the shape of an isosceles triangle, as shown in the accompanying diagram. What are the values of x and y? 1) 2) 3) 4) 12. In the diagram below of . What is 1) 5 2) 20 3) 25 4) 55 , side is extended to point D, , , and ? 13. Phil is cutting a triangular piece of tile. If the triangle is scalene, which set of numbers could represent the lengths of the sides? 1) 2) 3) 4) 14. On the banks of a river, surveyors marked locations A, B, and C. The measure of the measure of . Which expression shows the relationship between the lengths of the sides of this triangle? 1) 2) 3) 4) and 15. The diagram below shows the construction of the center of the circle circumscribed about This construction represents how to find the intersection of 1) the angle bisectors of 2) the medians to the sides of 3) the altitudes to the sides of 4) the perpendicular bisectors of the sides of 16. In shown below, P is the centroid and What is the length of 1) 6 2) 9 3) 3 4) 12 ? . . 17. The measures of five of the interior angles of a hexagon are 150°, 100°, 80°, 165°, and 150°. What is the measure of the sixth interior angle? 1) 75° 2) 80° 3) 105° 4) 180° 18. One piece of the birdhouse that Natalie is building is shaped like a regular pentagon, as shown in the accompanying diagram. If side AE is extended to point F, what is the measure of exterior angle DEF? 1) 36° 2) 72° 3) 108° 4) 144° 19. The measure of an interior angle of a regular polygon is 120°. How many sides does the polygon have? 1) 5 2) 6 3) 3 4) 4 20. If point 1) 2) 3) 4) is rotated counterclockwise 90° about the origin, its image will be point 21. What is the image of point 1) 2) 3) 4) after a reflection in the x-axis? 22. The image of point 1) 2) 3) 4) when reflected in the y-axis is 23. What are the coordinates of point P, the image of point 1) 2) 3) 4) 24. What is the image of point 1) 2) 3) 4) 25. A translation moves the same translation? 1) 2) 3) 4) 26. What is the image of point by a R90°? 1) 2) 3) 4) after a reflection in the line ? under a R180°? to . What are the coordinates of the image of point under after the composition of transformations defined by ry=x followed 27.A transformation of a polygon that always preserves both length and orientation is 1) dilation 2) translation 3) line reflection 4) glide reflection 27. When a dilation is performed on a hexagon, which property of the hexagon will not be preserved in its image? 1) parallelism 2) orientation 3) length of sides 4) measure of angles 28. What is the image of 1) 2) 3) 4) after a translation of 3 units right and 7 units down? 29. As shown in the diagram below, is a median of . Which statement is always true? 1) 2) 3) 4) 30. Given: , is the perpendicular bisector of Which statement can not always be proven? 1) 2) 3) 4) 31. What is the negation of the statement “Squares are parallelograms”? 1) Parallelograms are squares. 2) Parallelograms are not squares. 3) It is not the case that squares are parallelograms. 4) It is not the case that parallelograms are squares. 31. The statement “x is not the square of an integer and x is a multiple of 3” is true when x is equal to 1) 9 2) 18 3) 32 4) 36 32. Mary says, “The number I am thinking of is divisible by 2 or is divisible by 3.” Mary’s statement is false if the number she is thinking of is 1) 6 2) 8 3) 11 4) 15 33. The statement “If x is divisible by 8, then it is divisible by 6” is false if x equals 1) 6 2) 14 3) 32 4) 48 34. What is the inverse of the statement “If two triangles are not similar, their corresponding angles are not congruent”? 1) If two triangles are similar, their corresponding angles are not congruent. 2) If corresponding angles of two triangles are not congruent, the triangles are not similar. 3) If two triangles are similar, their corresponding angles are congruent. 4) If corresponding angles of two triangles are congruent, the triangles are similar. 35. What is the converse of the statement “If it is sunny, I will go swimming”? 1) If it is not sunny, I will not go swimming. 2) If I do not go swimming, then it is not sunny. 3) If I go swimming, it is sunny. 4) I will go swimming if and only if it is sunny. 36. 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. 37. Which statement is logically equivalent to “If I eat, then I live”? 1) If I live, then I eat. 2) If I eat, then I do not live. 3) I live if and only if I eat. 4) If I do not live, then I do not eat. 38. In the diagram below of To prove that 1) 2) 3) 4) and and , , and . are congruent by SAS, what other information is needed? 39. In the diagram of quadrilateral ABCD, Which method can be used to prove 1) AAS 2) SSA 3) SAS 4) HL , is congruent to , and diagonal ? is drawn. 40. In the diagram below, . Which statement must be true? 1) 2) 3) 4) 41. In the diagram below of , . Using this information, it could be proven that 1) 3) 2) 4) 42. Given: Prove: bisects at E. 43. Given: Prove: , bisects 44. Given: Prove: and , , C is the midpoint of and 45. Construct the median of ∆ABC to AC . B A C 46. Construct the altitude of ∆ABC to AC . B A C 47. In the diagram below of Point P must be the 1) centroid 2) circumcenter 3) incenter 4) orthocenter , , , and . 48. Which geometric principle is used in the construction shown below? 1) The intersection of the angle bisectors of a triangle is the center of the inscribed circle. 2) The intersection of the angle bisectors of a triangle is the center of the circumscribed circle. 3) The intersection of the perpendicular bisectors of the sides of a triangle is the center of the inscribed circle. 4) The intersection of the perpendicular bisectors of the sides of a triangle is the center of the circumscribed circle. 49. Triangle ABC has vertices , , and . Determine the point of intersection of the medians, and state its coordinates. [The use of the set of axes below is optional.] 50. The statement “If x is divisible by 8, then it is divisible by 6” is false if x equals 1) 6 2) 14 3) 32 4) 48 51. Which compound statement is true? 1) A square has four sides or a hexagon has eight sides. 2) A square has four sides and a hexagon has eight sides. 3) If a square has four sides, then a hexagon has eight sides. 4) A square has four sides if and only if a hexagon has eight sides. 52. Draw the image of ∆ABC after a reflection over line k. (You must use constructions with a compass.) A B C k under the translation along the vector 3,4 ? 53. What is the image of the point 1) 2) 3) 4) 54. Find the coordinates of the point P that lies along the directed line segment from A(1, 2) to B(10, 8) and partitions the segment in the ratio 2 to 1. 55. Find the coordinates of the point P that lies along the directed line segment from C(-3, -1) to D(7, 6) and partitions the segment in the ratio 3 to 2. 56. The diagram at right shows the intersection of three lines concurrent at the ______________ of a triangle. 1)incenter 2) circumcenter 3) centroid 4) orthocenter 57. For a triangle, which two points of concurrence could be located outside the triangle? 1) 2) 3) 4) incenter and centroid centroid and orthocenter incenter and circumcenter circumcenter and orthocenter 58. Which point is equidistant from the three sides of the triangle? 1) circumcenter (2) incenter (3) centroid (4) orthocenter 59. Determine a precise sequence of rigid motions which could be used to map triangle ABC onto triangle AB"C" . B" B C C" A