Basic Geometry Midterm Review 1 Match each definition with the correct term. 1 __________ Acute Angle A Two lines that are not coplanar and do not intersect 2 __________ Obtuse Angle B Ray or segment that splits an angle into two equal halves 3__________ Adjacent Angles C An angle greater than 90° and less than 180° 4 __________ Linear Pair D A triangle with (at least) two equal sides. 5 __________ Complementary Angles E A pair of non-adjacent angles formed by the intersection of two straight lines. These angles are always congruent. 6 __________ Vertical Angles F A set of points, lines, line segments, rays or any other geometrical shapes that lie on the same plane 7 __________ Supplementary Angles G An angle greater than 0° and less than 90° 8 __________ Angle Bisector H 3 or more points on the same line 9 __________ Isosceles Triangle I Two angles that are adjacent and supplementary 10 __________ Obtuse Triangle J Two angles whose sum is 180 11__________ Skew Lines K Triangle with one obtuse angle. 12__________ Coplanar L Two angles that share a common side and vertex and no common interior points 13_________ Collinear M Two angles whose sum is 90 Last Update 01/5/12 1 Basic Geometry Midterm Review 2 Use the diagram below and to the right for questions 14-16. Q 14.Which one the following is another name for AH ? D B K C A 15. Name a ray opposite AD 16.The intersection of plane P and plane Q is _____. H G 17. Draw segment BC ? 18 . Name this angle in 3 different ways. 19. Find mÐNLM and mÐKLM , if mÐNLM = (2x+9)ο°, mÐKLM = 52ο° and mÐNLK =75ο°. N M K 20. What is the vertex of ∠π·πΈπΉ? 21. What is the complement of 50 ° angle? 22. What is the supplement of 50 ° angle? L Questions 23 and 24 refer to the diagram to the right. 23. If π∠2 = 110° and π∠4 =(5x + 30) ο°, then the value of x is ____. 1 2 3 4 24. If mÐ1= 60 ο° and mÐ2 = (3x + 15) ο°, then the value of x is _____. Last Update 01/5/12 2 P Basic Geometry Midterm Review 3 25. SQ bisects ÐRST . Find the measure of ÐQST if mÐRST = 50ο°. T Q S R 26. Which one of the following is the converse of: "If two segments have the same measure, then they are congruent." 27. In the diagram to the right, find π∠1 and π∠2. 130° 80° Use the diagram to answer questions 28-29. r 28. If r s , Ð3then is congruent to ________. b 9 1 2 4 3 c 29. If∠8 ≅ ∠16, then ________. s 5 6 8 7 10 11 12 13 14 16 15 Use the diagram to answer questions 30-31. 30. If b c , then ∠4 must be ________ to ∠5 r 31. If c b, then ∠2 is congruent to ________. b c 32. Find x if AB CD , π∠7= (5x+60)ο°, and π∠1 =70ο°. A 9 1 2 4 3 13 14 16 15 B 2 1 4 5 3 D 6 7 Last Update 01/5/12 10 11 12 5 6 8 7 3 C s 8 Basic Geometry Midterm Review 4 33. What are the measures of the angles in an equilateral triangle? 34. If two angles of a triangle have measures 25ο° and 75ο°, what is the measure of the third angle? 35. How many rights angles can any given triangle have? 36. Use the markings on the diagram to determine why ADB @ CDB . C B A 37. If PQR @ D π΅π· ______. DBF (not shown), then Μ Μ Μ Μ 38. Determine what information you would need to know in order to use the ASA Postulate to show that the triangles are congruent. A D B C 39. In JKL (not shown), KL @ JL , mÐK = 70, mÐL = 40. Find mÐJ . Hint – Draw triangle to help solve. 40. If π΄π΅ ≅ Μ Μ Μ Μ π·πΈ because ____________. ABC @ DEF , then you can say Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ 41. Given ABC @ XYZ , BC=40 and XY=5x+10, find the value of x. 42. Name the 5 ways of proving a triangle congruent. For questions 43-46, state which of the postulates or theorems could be used to justify the conclusion. Μ Μ Μ Μ and E is the midpoint of π·πΊ Μ Μ Μ Μ , then βπ·π»πΈ ≅ Μ Μ Μ Μ ⊥ π·πΊ 43. If π»πΈ βπΊπ»πΈ by ___________. Last Update 01/5/12 4 Basic Geometry Midterm Review 5 Μ Μ Μ Μ = π»π· Μ Μ Μ Μ , then βπ·π»πΈ ≅ βπΊπ»πΈ Μ Μ Μ Μ and Μ Μ Μ Μ 44. If π»πΊ π·πΈ = πΈπΊ by ___________. T 45. Name the additional pairs of corresponding parts that need to be congruent in order to prove that FIG @ TOM by ASA. F O G I M 46. The base angles of an isosceles triangle are always _____________. 47. Find mÐ2 . 70° 30° 48. Find mÐ3 3 2 1 49. Find mÐ1 B 50. Which segment is an altitude of 51. Which segment is a median of Last Update 01/5/12 ABC ? ABC ? E A 5 C D Basic Geometry Midterm Review 6 For questions 54-59, choose the option that specifies the statement or reason in the following proof: B ^ Given: BD AC D is the midpoint of AC Prove: A C Proof: D Statements 1. 2. 3. 4. 5. 6. 7. BD Reasons ^ AC οADB ≅ οCDB D is the midpoint of AC AD = DC BD @ DB D ABD @ __________{Q55} __________ ∠π΄ ≅ ∠πΆ 52. A. def. of midpoint 53. A. def. of right B. Given Ð B. def of ^ lines 1. 2. 3. 4. 7. 8. 9. Given __________{Q52} __________ Given __________{Q53} __________ __________{Q54} __________ __________{Q56} __________ __________{Q57} __________ C. def of ^ lines D. def of segment C def. of midpoint D. def of vertical Ð ’s 54. A. Reflexive Prop. B. Symmetric Prop. C. def of @ segments C. βπ΄π΅πΆ D. def. of midpoint 55. A.βπ·πΆπ΅ B. βπΆπ΅π· D. βπ΅πΆπ· 56. A. SSS Post. B. SAS Post. C. ASA Post. D. CPCTC 57. A. SSS Post. B. SAS Post. C. ASA Post. D. CPCTC 58. If two sides of a triangle have the following measures, find the range of possible measures for the third side. 4, 8 59. Determine if the three numbers can be measures of the sides of a triangle. 4, 7, 8? 60. Determine if the three numbers can be measures of the sides of a triangle. 8, 11, 22? Last Update 01/5/12 6 Basic Geometry Midterm Review 7 61. If D is the midpoint of Μ Μ Μ Μ π΄π΅ and E is the Μ Μ Μ Μ find the length of Μ Μ Μ Μ Μ Μ Μ Μ = 12. midpoint of π΄πΆ π·πΈ . π΅πΆ 62. If 6+π₯ π₯ 8 = 5, then what is the value of x? Μ Μ Μ Μ = 8.4, 63. Δπ΄π΅πΆ ~ βπ·πΈπΉ, if Μ Μ Μ Μ π΄π΅ = 6, Μ Μ Μ Μ π΄πΆ = 8, π΅πΆ Μ Μ Μ Μ = 5.4, what is the measure of Μ Μ Μ Μ πππ π·πΉ π·πΈ . 64. If b = 6 and c = 10, what is the length of a? Classify the triangles in numbers 67 – 69 as acute, obtuse or right. 65. 6, 7, 8 66. 6, 8, 10 67. 9, 12, 17 Find the value of x and y. 68. x = B y 60° 7 69. y = 30° A Last Update 01/5/12 7 x C Basic Geometry Midterm Review 8 Find the value of a and b. 70. a = 45° b 71. b = 72. What is the sum of the exterior angles in a convex 12-sided polygon? 5 a 73. What is the sum of the interior angles of a 12- sided polygon? 74. What is the measure of each angle of a regular 8-sided polygon? 75. What is the distance between point R and point S? 76. Point J is located at (1,3) and point K is located (5,-3). Find the midpoint of line segment JK. Last Update 01/5/12 8