A calculator and patty paper may be used. A compass and straightedge is required. The formulas below will be provided in the examination booklet.

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 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 degree measures of the interior angles of a polygon: oordinate Geometry Formulas Let and be two points in the plane. slope = egree measure of an interior angle of a regular polygon: midpoint = distance = MPS

2 1. Name the three undefined terms of geometry. 2. How many different lines are determined by two points? 3. How many different lines are determined by three noncollinear points? 4. How many different planes are determined by three noncollinear points or by two intersecting lines? 5. 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? 6. On a number line, points,, and have coordinates a, b, and c with a b c. If a 9, 21, and 2, what are the values of b and c? For items 7 through 10, points,, and are on a number line, with between and. 7. If = 10 and = 20, then = 8. If = 20 and = 12, then = 9. If = x, = 2x 30, and = 90, then x = 10. If = 2x 10, =5x 40, and =9x 70, what is the length of? For items 11 through 14, points,, and are collinear, with the midpoint of. 11. If = 6, then = 12. If = 3x 20and = 50, then x = 13. If = 4x 20and = 6x 30, then x = 14. If = 5x 30and =12x 10, then x = 15. 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? MPS

3 Look at the drawing below. 16. If m o, what is the measure of m 2? 17. If m 1 4x 20 o and m 2 x 10 o, what is the value of x? 18. If m 1 6x 38 o and m 2 4x 22, what is m 1? 19. In the figure below,, (2 20) o o m x and m (4x 40). o 1 2 a. What is the value of x? b. What is the measure of? 20. Look at the figure below. 4xo y o 40 o 3x o Find the values of x and y. For items 21 through 25, write a rule in the form F x, y?,? that describes the given transformations. 21. x, y is reflected about the x-axis. 22. x, yis reflected about the y-axis. 23. x, yis reflected about the line y = x 24. x, yis rotated 180 degrees about the origin. 25. x, yis translated five units right and three units down. MPS

4 26. 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 27. 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

5 28. 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. For the conditional If an animal is a dog, then the animal is warmblooded, which statement is true, its converse, its inverse, or its contrapositive? 29. Look at the conditional below. If I am between the ages of 13 and 19, 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. For the conditional If I am between the ages of 13 and 19, then I am a teenager, which statement(s) are true, its converse, its inverse, or its contrapositive? 30. 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. 31. Look at the statements below. If hris earns at least $10, then he will go to the game. If hris goes to the game, then he will bring Jane. hris earns $12. Write all valid conclusions from the statements above. MPS

6 For items 32 and 33, write a valid conclusion from the statements. 32. If a triangle is equilateral, then it is equiangular. Triangle is equilateral. 33. If Sally studies for a test, then she will pass the test. Sally does not pass the test. 34. 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 For items 35 through 38, state whether inductive reasoning or deductive reasoning is used. 35. The ubs have not won a World Series in 104 years. Therefore, they will not win this year. 36. ll squares have congruent diagonals. If I construct a square, the diagonals will be congruent. 37. If an animal is a black bear, it will hibernate in the winter. I spotted a black bear; I concluded that the bear will hibernate this winter. 38. I saw a pattern as follows: 12, 11, 14, 9, 16, 7. I concluded that the next two terms in the pattern are 18, Make a logical chain from these statements. If I go to the store, then I will buy candy. If I buy candy, then I will not eat my dinner. If it is sunny outside today, then I will go to the store. 40. Make a logical chain from these statements. If I get a reward, then it will be a video game. If I do my homework, then I will do well on my test. If I do well on my test, then I will get a reward. If I listen carefully in class, then I will do my homework. 41. etermine the number of lines of symmetry that each figure has. a. square b. regular octagon c. circle MPS

7 42. raw any lines of symmetry on the figure below. 43. 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 44. 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

8 45. In the figure below, p q r. 55 o p x o 40 o q r What is the value of x? 46. Find the value of x and y in the figure below. MPS

9 47. 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. 48. Look at isosceles triangle below. 120 o What are the values of x and y? 49. Look at the triangle below. c o 15 Which of the following statements is true about a, b, and c? b a c b c a c a b a c b a o b o MPS

10 For items 50 through 53, grid-in and bubble your answers. 50. Find the sum of the interior angles of a pentagon. 51. Find the measure of each interior angle of a regular 15-sided polygon. 52. etermine the measure of each exterior angle of a regular 9-sided polygon. 53. The measure of each exterior angle of a regular polygon is 45 o. How many sides does the polygon have? The measure of each interior angle of a regular polygon is 120 o. How many sides does the polygon have? 55. 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 MPS

11 57. 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 58 through 61, find the value of x and/or y in each figure x y x drawn to scale x MPS

12 62. 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. 63. 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. 64. 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. 65. In a coordinate plane, point has coordinates 2,9 and point has coordinates 5,17. What are the coordinates of the midpoint of? 66. 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 F a. EF, F, F b. F, E, c. F, E, EF d. EF, F, E e. E, F, E f., F, EF MPS

13 67. Given: is the perpendicular bisector of. Prove: E 68. Given: EG FG Prove: F GF E F G H 69. 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 70. 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 MPS

14 71. 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 72. 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