Geometry Formula Sheet First Semester Exam

Transcription

1 Geometry Semester Eam Information: The semester eam will cover material from chapters 1-5. It will be worth 20% of your first semester grade. It consists of 70 true false and multiple-choice questions. Studying previous tests and quizzes is an ecellent way to prepare, as well as doing the attached study guide. The attached questions must be turned in on the day of your eam (as you arrive at class.) They must be done neatly on separate sheets of paper, and you must show work on starred (***) problems. I WILL NOT ACCEPT LATE REVIEWS! These review questions will be worth 10% of your eam grade. You need to start preparing now so you have time to look up and ask about problems you don t understand. There will be a few days in class to work on these as well. Here is the eam schedule. Tue, Jan 11 Wed, Jan 12 Thu, Jan 13 Fri, Jan 14 8:20-8:55 Period 1 9:00-9:40 Period 2 8:20-10:20 Period 1 Eam Period 2 Eam Period 3 Eam 9: - 10:25 Period 3 10:30-11:00 Period 4 (1 st lunch) Period 5 (1 st lunch) Period 6 (1 st lunch) 10:30-11:00 Period 7 (1 st lunch) 11:00-11:30 Period 4 (2 nd lunch) Period 5 (2 nd lunch) Period 6 (2 nd lunch) 11:00-11:30 Period 7 (2 nd lunch) 11:35-1:30 Period 4 Eam Period 5 Eam Period 6 Eam 11:35-1:30 Period 7 Eam 1:35-3:20 Make-up Eam Make-up Eam Make-up Eam 1:35-3:20 Make-up Work You will be given the following formula sheet for your eam: Slope: Geometry Formula Sheet First Semester Eam Midpoint: Distance: Point Slope Form of a Line: Slope Intercept Form of a Line:

2 Review Questions: To be done on separate sheets of paper (it is not necessary to copy problems, but work must be shown on starred (***) problems.) The number in parentheses at the end of the problem tells which chapter it comes from. 1. points are always collinear (give the largest number.) (1) 2. points are always coplanar (give the largest number.) (1) 3. What figure is formed by the intersection of two lines? (1) 4. What figure is formed by the intersection of two planes? (1) 5. What figure is formed by the intersection of a line and a plane? (1) 6. Define supplementary and complimentary angles. (1) 7. What is special about two angles that form a linear pair? (2) 8. What is special about vertical angles? (2) 9. When two lines are parallel and cut by a transversal, which angle pairs are congruent? Which are supplementary? (Multiple answers list all of them.) (3) 10. A triangle has no congruent sides. (4) 11. A triangle has at least two congruent sides. (4) 12. A triangle has all sides congruent. (4) 13. What is significant about the angles in an isosceles triangle? (4) 14. What is significant about the angles in an equilateral triangle (be as specific as possible)? (4) 15. Could a triangle have sides of length 2, 3, and 4? Justify your answer. (5) 16. Could a triangle have sides of length 15, 15, 30? Justify your answer. (5) 17. Could a triangle have sides of length 4, 5, and 10? Justify your answer. (5) 18. What are the possible lengths of the third side of a triangle with sides 20 and 30? (5) 19. Eplain the difference between the notations. (1) 20. Sketch triangle ABC with median. (5) 21. Sketch triangle MNP with altitude. (5) 22. Sketch triangle XYZ with angle bisector. (5) 23. Sketch triangle KLM with the perpendicular bisector of LN. (5) 24. Sketch a triangle RST with a midsegment parallel to (5) 25. Consider SSS, SAS, ASA, AAS, SSA, AAA, HL? Which of them can be used to prove triangles are congruent? Which cannot be? (4) 26. Consider the conditional statement If = y, then a = b. Write the converse, inverse, and contrapositive. (2) 27. If a conditional statement is true, what else must be true? (2) 28. If the converse of a statement is true, what else must be true? (2) 29. In the figure at the right, name two pairs of supplementary angles. (1) 30. Name two pairs of complementary angles. (1) 31. Name two pairs of adjacent angles. (1) 32. Name one pair of vertical angles. (1) 33. Name two linear pairs. (1) 34. If ΔMNP ΔQRS, name all pairs of congruent sides and angles. (4) 35. Write down the distance formula. (1) 36. Write down the slope formula. (3) 37. Write down the midpoint formula. (1) T S W 90 P R Q

3 38. *** Find the distance between the points (3, 2) and (-1, 4). Round to the nearest hundredth. (1) 39. *** Find the slope of the line connecting the points (4, -1) and (-2, 6). Write it as a reduced fraction. (3) 40. What is the slope of a line parallel to the line in #39? (3) 41. What is the slope of a line perpendicular to the line in #39? (3) 42. *** Find the midpoint of the segment connecting (3, 1) and (-5, -2). (1) 43. *** A is (1, 4) and M is (3, -2). If M is the midpoint of, find the coordinates of B. (1) 44. In the figure at the right, are S, Q, R, and V coplanar? (1). Name the marked points in both planes A and B. (1) 46. What is the intersection of planes A and B? (1) 47. Name two points collinear with V. (1) 48. What does CPCTC stand for? (4) 49. Eplain the concept of CPCTC. (4) 50. Using the figure at the right, name the transversal. (3) 51. Name a pair of corresponding angles. (3) 52. Name a pair of alternate interior angles. (3) 53. Name a pair of alternate eterior angles. (3) 54. Name a pair of same-side interior angles. (3) 55. Name a linear pair. (1) 56. Name a pair of vertical angles. (1) 57. In ΔABC, m A = 30 and m B = 130. Sketch the triangle, find and list the sides in increasing order. (5) 58. In ΔMNF, MN = 5, NP = 10, and MP = 13. Sketch the triangle and list the angles in increasing order. (5) 59. *** The eterior angle at the base of an isosceles triangle is 150. Find the measures of all three interior angles. (4) 60. *** Two angles that form a linear pair have measures of and Find the measure of each angle. (2) 61. *** The three angles of a triangle have measures of + 8, 2, and Find the measure of each angle. (4) 62. *** Find the equation of a line in point-slope form that passes through (3, 2) and (-1, 8) (3) 63. *** Find the equation of a line in slope-intercept form that has a slope of -3 and passes through (3, -2). (3) 64. *** Determine whether the lines 2 + 3y = 9 and 4 + 6y = 18 are parallel, perpendicular, intersecting but not perpendicular, or coincident. (3) 65. *** Determine whether the lines y = and 4 2y = 8 are parallel, perpendicular, intersecting but not perpendicular, or coincident. (3)

4 In the following problems, find in reduced radical form. Show work. (All in chapter 5.) *66. * *68. * In the figure at the right, B, F, and D are midpoints. (Ch. 5) A 70. CE =? 71. FD =? 72. BD =? 73. m E =? 74. m BDF =? 75. m DFB =? 4cm B 55 3cm F 12 cm 65 C D E Tell whether each represents a translation, reflection, or rotation. (Ch 1)

5 A 79. Complete the following proof. (Ch. 4) 1 2 Given:, 3 4 Prove: P Q Statements P M Q Reasons 1., ΔAPM ΔAQM P Q In the following proof, the statements are in the wrong order. List the correct order. (Ch. 4) Given:, D and X are right angles, E Y E Y Prove: D Z F X Statements A. ΔEFD ΔYZX B. 1 2 C., D and X are right angles, E Y D. D X