A calculator, scrap paper, and patty paper may be used. A compass and straightedge is required.

Transcription

1 The Geometry and Honors Geometry Semester examination will have the following types of questions: Selected Response Student Produced Response (Grid-in) Short nswer calculator, scrap paper, and patty paper may be used. compass and straightedge is required. The formulas below will be provided in the examination booklet. Polygon ngle Formulas Let n be the number of sides of a polygon. Sum of the degrees of the interior angle of a polygon: egree measure of an interior angle of a regular polygon: oordinate Geometry Formulas Let be two points in the coordinate plane. Slope = Midpoint = istance = MPS

2 1. Name the three undefined terms of geometry. 2. omplete the following with always, sometimes, or never. a. Two points are collinear. b. Two points are coplanar. c. Three points are collinear. d. Three points are coplanar. 3. How many different lines are determined by two points? 4. How many different lines are determined by three noncollinear points? 5. How many different planes are determined by three noncollinear points? 6. How many planes are determined by two intersecting lines? 7. Which of the following statements are true about figures in space? a. line and a plane could have no points in common. b. line and a plane could have one point in common. c. line and a plane could have an infinite number of points in common. d. Two distinct planes could have no points in common. e. Two planes could have a line in common. 8. On a number line, point has coordinate 5, and point is on the line such that = 8. What are the two possible coordinates of point? 9. Let., and be points on a number line with respective coordinates a, b, and c such that a b c. If b 6, 30,and 2, then what are the coordinates of a and c? For items 10 through 12, points,, and are on a number line, with between and. 10. If = 20 and = 12, then = 11. If = x, = 2x 30, and = 90, then x = 12. If = 2x 10, =5x 40, and =9x 70, what is the length of? MPS

3 For items 13 through 16, points,, and are collinear, with the midpoint of. 13. If = 6, then = 14. If = 3x 20and = 50, then x = 15. If = 4x 20and = 6x 30, then x = 16. If = 5x 30and =12x 10, then x = 17. Points E, F, G, H lie on a line, in that order. a. If EF GH, name another pair of congruent segments. b. If EF GH, EH 50, FG 36, what is the length of EG? For items 18 through 20, use the drawing at the right. Grid-in and bubble answers on the grids below If m o, what is the measure of m 2? 19. If m 1 4x 20 o and m 2 x 10, what is the value of x? 20. If m 1 6x 38 o and m 2 4x 22, what is m 1? o o MPS

4 o 21. In the figure below,, m 2x 20 and m 4x 40. o Figure NOT drawn to scale a. What is the value of x? b. What is the measure of? 22. Look at the figure below 4x o 3x o 40 o y o Figure NOT drawn to scale Find the values of x and y. For items 23 through 28, write a rule in the form F x, y?,? that describes the given transformations. 23. x, y is reflected about the x-axis. 24. x, yis reflected about the y-axis. 25. x, yis reflected about the line y = x 26. x, yis rotated 180 degrees about the origin. 27. x, yis translated five units right and three units down. 28. x, yis translated six units left, then reflected across the y-axis. MPS

5 29. Which of the following terms describes transformations, such as reflections, rotations, and translations, in which the preimage and image are congruent? ongruent Similar Rigid Regular 30. Look at the parallelogram on the coordinate plane below. y Each square represents one unit x a. Reflect across the y-axis. Name the reflected figure. b. Translate four units downward. Name the translated figure. c. Write the coordinates of and. d. If P x, y is on, what are the coordinates of the transformed point on? Explain how you determined your answer. Use words, symbols, or both in your explanation. MPS

6 31. Look at the conditional below. If an animal is a dog, then the animal is warm-blooded. a. raw an Euler diagram for this conditional. b. Write the converse of the conditional. c. Write the inverse of the conditional. d. Write the contrapositive of the conditional. e. Which statement(s), converse, inverse, or contrapositive are true regarding the statement If an animal is a dog, then the animal is warm-blooded. 32. Look at the conditional below. If I am between 13 and 19 years old, inclusive, then I am a teenager. a. Write the converse of the conditional. b. Write the inverse of the conditional. c. Write the contrapositive of the conditional. d. Which statement(s), converse, inverse, or contrapositive are true regarding the conditional If I am between 13 and 19 years old, inclusive, then I am a teenager. 33. Look at the following statement. If you are 19 years old, then you can vote. a. raw an Euler diagram for this conditional. b. Use the Euler diagram to evaluate the statement: If you vote then you are 19 years old. MPS

7 34. Let p : hris earns $20 q : hris buys gas r : hris drives to Rockville ssume the following premises: p q q r For each premise below, write the conclusion(s) in words, if any, which follows. a. p b. q c. p d. q e. r For items 35 and 36, write a valid conclusion from the following statements. 35. If a triangle is equilateral, then it is equiangular. Triangle is equilateral. 36. If Sally studies for a test, then she will pass the test. Sally does not pass the test. 37. Look at the statements below. If hris earns $10, then he will go to the game. If hris goes to the game, then he will bring Jane. hris earned $12. Write all valid conclusions from the statements above. 38. How is a truth table used to determine whether two statements are logically equivalent? MPS

8 39. omplete the following truth table. P Q P P Q P Q P Q T T T F F T F F 40. omplete the following truth table. P Q T T T F F T F F P Q Q P 41. Which of the following are logically equivalent? statement and its converse statement and its inverse statement and its contrapositive statement, its converse, its inverse, and its contrapositive 42. proof by contradiction is another name for an proof. 43. Suppose you wish to prove the following using indirect proof. If two parallel lines are cut by a transversal, then the alternate interior angles are congruent. Which of the following would you try to contradict in an indirect proof? Suppose two parallel lines are cut by a transversal. Suppose alternate interior angles are congruent. Suppose alternate interior angles are not congruent. Suppose two parallel lines are not cut by a transversal. MPS

9 44. omplete the following using indirect reasoning. If I earn $20 this week, then I will go to a movie. I did not go to a movie. therefore, For items 45 through 49, state whether inductive reasoning or deductive reasoning is used. 45. If Mr. Johns was absent on Monday, Tuesday, and Wednesday, I conclude that he will be absent on Thursday. 46. The ubs have not won a World Series in 104 years. Therefore, they will not win this year. 47. ll squares have congruent diagonals. If I construct a square, the diagonals will be congruent. 48. If an animal is a black bear, it will hibernate in the winter. I spotted a black bear; I concluded that the black bear will hibernate this winter. 49. I saw a pattern as follows: 18, 11, 20, 9, 22, 7. I concluded that the next two terms are 24, Make a logical chain from these statements. If I go to the store, I will buy candy. If I buy candy, I will not eat my dinner. If it is sunny outside today, I will go to the store. 51. Make a logical chain from the following statements. If I get a reward, then I will buy new car. If I do well on the next test, then I will get a reward. If I buy a new car, then it will have four-wheel drive. If I do my homework, then I will do well on the next test. 52. etermine the number of lines of symmetry that each figure has. a. square b. regular octagon c. circle 53. harlie states that the number of degrees of rotational symmetry for a regular hexagon is always a multiple of 60 o (0 o, 60 o, 120 o, 180 o, ). Is harlie correct? Use mathematics to justify your answer. MPS

10 54. Look at the regular pentagon below. Which of the following is NOT a possible measure of the pentagon s rotational symmetry? 36 o 72 o 144 o 216 o 55. Place an X in the boxes where the property is true. Opposite sides congruent Property Parallelogram Rectangle Square Rhombus Trapezoid Only one pair of opposite sides are parallel Opposite angles congruent Each diagonal forms 2 congruent triangles iagonals bisect each other iagonals congruent iagonals perpendicular diagonal bisects two angles ll angles are right angles ll sides are congruent MPS

11 56. In the figure below, p q r. Figure NOT drawn to scale 55 o p x o 40 o q r What is the value of x? 57. Find the value of x and y in the figure below. Figure NOT drawn to scale MPS

12 58. Look at the figure below. l m n 2 p For each of statement below, state which lines can be proven parallel. Justify your answer. a. 1 2 b. 3 4 c. 4 and 5 are supplementary. 59. Look at isosceles triangle below. 120 o Figure NOT drawn to scale What is the value of x? 60. Look at the triangle below. a x o b y o c If a b c, then what is the relationship between x, y,and z? x y z y x z x z y z y x z o MPS

13 61. Find the sum of the interior angles of a pentagon. 62. Find the measure of each interior angle of a regular 15-sided polygon. 63. etermine the measure of each exterior angle of a regular 9-sided polygon. 64. The measure of each exterior angle of a regular polygon is 45 o. How many sides does the polygon have? 65. The measure of each interior angle of a regular polygon is 120 o. How many sides does the polygon have? 66. Two sides of a triangle measure 6 and 9. ircle the possible values of the length of the third side Find the value of y in the figure below. y o 30 y o 80 y o Figure NOT drawn to scale 68. What is the difference in the measures of an interior angle of a regular pentagon, and an exterior angle of a regular pentagon? For items 69 and 70, find the value of x in each figure. 69. Figure NOT drawn to scale Figure NOT drawn to scale x MPS

14 71. Graph the points 3,2, 1, 2, 2, 5, 4, 1 on the coordinate plane. What kind of quadrilateral is? Use mathematics to justify your answer. 72. Points 3, 1, 1,1, and 1,1 are three vertices of a parallelogram. a. How many parallelograms can be formed using these three points? b. Give the coordinates of the fourth vertex of the other parallelograms. 73. triangle has vertices 3,4, 4,6, 7,18. Use slopes to determine whether the triangle is a right triangle. Justify your answer using mathematics. 74. In a coordinate plane, point has coordinates 2,9 and point has coordinates 5,17. What are the coordinates of the midpoint of? 75. For each figure below, determine which congruence postulate or theorem can be used to prove the triangles congruent. If the triangles cannot be proven congruent, state that fact. E Figure NOT drawn to scale F a. EF, F, F b. F, E, c. F, E, EF d. EF, F, E e. E, F, E f., F, EF MPS

15 76. Given: is the perpendicular bisector of. Prove: E 77. Given: E Prove: E E 78. Given: EG FG Prove: F GF E F G H 79. Quadrilateral PQRS has diagonals PR and QS that intersect at point T. For the conditions given below, state whether the quadrilateral is a rhombus, rectangle, parallelogram, or none of these figures. a. PS QR, PS QR b. PQRS is a parallelogram, PR QS c. PQRS is a parallelogram, PR QS d. QP RS MPS

16 80. Perform the following constructions. Use mathematics to justify each construction. a. The perpendicular bisector of a segment b. The bisector of an angle c. line parallel to a given line, through a point not on the line d. point equidistant from three given points 81. Point P is on the angle bisector of. Which of the following statements is true? I Point P is equidistant from and. II P P Neither I nor II I only II only oth I and II 82. Point P is on the perpendicular bisector of. Which of the following statements is true? I P P 1 II P 2 Neither I nor II I only II only oth I and II MPS