Geometry: T1 REVIEW. Name: Class: Date: ID: A. 1. Name three points in the diagram that are not collinear. AB = x + 16, BC = 5x + 10, AC = 56

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1 Name: Class: Date: ID: A Geometry: T1 REVIEW 1. Name three points in the diagram that are not collinear. AB = x + 16, BC = 5x + 10, AC = Find AB and BC in the situation shown above. 2. Name a ray from Q through P. 3. Describe what the notation RS Illustrate with a sketch. stands for. 4. Draw a plane that intersects two other planes. 5. Two distinct planes intersect. Describe their intersection. Draw a sketch to support your answer. 10. T is the midpoint of PQ. Which one of the following is not an appropriate statement? a. PT = TQ b. PT = TQ c. PT TQ d. PT + TQ = PQ 11. Point S is between points R and T. P is the midpoint of RS. RT = 20 and PS = 4. Draw a sketch to show the relationship between the specified segments. Find ST. AB = 2x + 17, BC = 5x 10, AB = BC 6. Sketch the intersection of a line and a plane. 7. If AB = 19 and AC = 32, find the length of BC. 12. Find AB and BC in the situation shown above. 8. If AB = 17 and AC = 22, find BC. 1

2 13. Which angle measures approximately 72? a. 16. If m JOK = 28 and m JOL = 58, then what is the measure of KOL? b. c. 17. m OMN = (2x + 9) and m LMN = (6x 7) and m OML = 66. Find m OMN and m LMN. d. 14. Which does not name the angle below? 18. Classify the angle as right, acute, or obtuse. a. DCE b. CDE c. ECD d. C 15. If P Q and m Q = 67, then m P =. 19. The measure of angle A is 98. Classify angle A as an acute, right, or obtuse angle. 20. Find the measures of PMN and NMR if MN bisects PMR. The measure of PMR is 108. Draw a sketch that shows the given information. 21. AB bisects LAX and LAB measures 68. Find the measure of XAB. 2

3 22. Name this angle in three different ways. 27. Name a pair of vertical angles in the figure above. 28. Complete the conditional statement to make a true statement. 23. If G and H are supplementary and m H = 67, then. 24. In the figure shown, m AED = 108. True or False: AEB and AED are vertical angles and m AEB = 72. Name an angle supplementary to 2 in the figure above. 29. Which figure below is not a polygon? a. b. c. 25. Solve for x: d and 2 form a linear pair. m 1=73. Find m 2. 3

4 30. Which figure below is not a convex polygon? a. 32. Which figure below is not a regular polygon? a. b. b. c. c. d. d. 31. Which one of the statements below is false? a. A circle is NOT a polygon. b. An octagon has 8 angles. c. A decagon has 10 sides. d. A pentagon has 9 angles. 33. Complete the statement. A regular polygon is both and equiangular. 34. Explain why the figure shown does not satisfy the definition of a polygon. 35. Sketch a polygon that is concave and has five sides. 36. Sketch a five-sided polygon that is convex. 37. Name a polygon with 10 sides. 4

5 38. Name the regular polygon. 44. Find the area and circumference of the circle. Use π = The lengths (in inches) of two sides of a regular octagon are represented by the expressions 2x + 4 and 3x 8. Find the length of a side of the octagon. 40. The expressions ( 3x + 18) û and ( 5x 42) û represent two angle measures of a regular pentagon. Find the measure of an angle of the pentagon. 41. Determine if the figure below is a regular polygon. If it is not a regular polygon, explain why. 45. Find the area: 46. A play yard is 26 ft by 29 ft. A fence is to be built around the yard. How many feet of fencing will be needed? If fencing costs $5.50 per foot, what will be the cost of the fence? 47. The figure below represents which of the following statements? Use the formula for the area of a triangle (A = 1 bh) to find the value of the unknown 2 variable. 42. A = _, b = 6cm, h = 10 m 43. A = 15 ft 2, b =5 ft, h = a. Two rays that are perpendicular b. A straight angle c. AB = AC d. Two lines that are perpendicular 48. "If I am invited, then I will go." What is the underlined portion called in this conditional statement? 5

6 49. "If it doesn t rain, then I will go to the game." What is the underlined portion called in this conditional statement? True or False: 51. Line l bisects GBJ. 52. Line n bisects DE. 53. FBG and FBJ are complementary. 54. BF is perpendicular to line m. 55. Points D, J, and F are collinear. 50. Points D, J, and E are coplanar. 56. Identify the hypothesis and conclusion of the statement. If today is Wednesday, then tomorrow is Thursday. 57. "If an obtuse angle is bisected, then two acute angles are obtained." Write the converse of this conditional statement. Is the converse true? 58. Tell whether the following statement is True or False. If it is false, give a counterexample. "If a number is even, then it is a multiple of 4." 61. Write the inverse of the following statement. If a number is not even, then it is not divisible by two. Decide whether the statement about the diagram is true. Explain your answer using definitions you have learned. Write the converse of the following statement(s). Then tell whether the converse is True or False. 59. If a statement is true, then its converse is false. Rewrite the following conditional statement in if-then form. 60. Every pair of odd numbers has a difference that is an even number. 62. m AEB = 90 û 63. m BEC = 30 û 64. BEC and CED are a linear pair. 65. Given that: i. No people who run for office are reliable. ii. All politicians run for office. What conclusion can be logically deduced? 6

7 From the given true statements, make a valid conclusion: 66. If Ahmed can get time off work, he will go to Belize. If Ahmed goes to Belize, Jake will go with him. Ahmed will get time off work. 67. If there is no more milk, Rita will go to the store. There is no more milk. 68. If the slipper fits, she is the one. Cinderella fits in the slipper. Write the conclusion to be drawn from the two pieces of given information: 69. Supplementary angles have measures with a sum of 180. C and D are not supplementary. 70. Given the following statements, can you conclude that Marvin listens to the radio on Monday night? (1) If it is Monday night, Marvin stays at home. (2) If Marvin stays at home, he listens to the radio. 71. For the past 6 weeks, your aunt has asked you to watch your cousin on Wednesday night. You conclude that you will be asked to watch your cousin next Wednesday. Use the diagram to write an example of the postulate State the postulate indicated by the diagram. 75. Through any two points there exists exactly one line. 76. If two lines intersect, then their intersection is exactly one point. 77. Which of the following is an example of the Transitive Property? a. If y = x 4, then x 4 = y. b. x 3 = x 3 c. If x = 3, then x 4 = 3 4. d. If x 3 = y and y = 4, then x 3 = Name the property which justifies the following conclusion: Given: b + c d = e and d = a Conclusion: b + c a = e 7

8 79. Name the property which justifies the following conclusion: Given: 18x = 288 Conclusion: x = Provide the reasons for each statement in the proof. Given: AB = DE Prove: AD = BE Identify the property that makes the statement true. 80. If XY = MN, then MN = XY. 81. If m P = m R and m R = m T, then m P = m T. 82. If MP = PQ and PQ = QR, then MP = QR. 83. If m 1 + m 2 = 25 and m 1 = 9, then 9 o + m 2 = 25 o. Statement Reason AB = DE? AB + BD = DE + BD? AB + BD = AD, DE + BD = BE? AD = BE? 85. Provide the reasons for each statement in the proof. Given: m 1 = m 3, m 2 = m 4 Prove: m AFC = m EFC Statement Reason m 1 = m 3, m 2 = m 4? m 1 + m 2 = m 3 + m 2 m 1 + m 2 = m 3 + m 4?? m 1 + m 2 = m AFC, m 3 + m 4 = m EFC? m AFC = m EFC? 8

9 86. In the figure shown, m AED = 124. Which of the following statements is false? and 2 are supplementary angles. 1 and 3 are vertical angles. m 2=67. Find m 3. a. BEC and CED are adjacent angles. b. AEB and DEC are supplementary angles. c. m AEB = 56 d. m BEC = Provide the reasons for statements 3 and 5 in the proof. Given: 1 and 2 form a linear pair; m 2=100 Prove: m 1=80 Statements Reasons 1. m 2 = Given 2. 1 and 2 are a linear pair. 2. Given 3. m 1 + m 2 = ? 4. m = Substitution Property of Equality 5. m 1 = 80 5.? 89. a. Find and describe a real-world example of each of the following: parallel lines, intersecting lines, skew lines, parallel planes, and intersecting planes. b. Why do you think there are no skew planes? 90. In the figure, l Ä n and r is a transversal. Which of the following is not necessarily true? a. 8 2 b. 2 6 c. 5 3 d

10 91. In the figure shown, HC Ä GD and m ABC = 100. Which of the following statements is false? 95. Use the figure to find the measure of 4. a. m CBE = 80 b. m DEF = 80 c. DEB and CBE are corresponding angles. d. CBE and GEB are alternate interior angles. 92. Line m is parallel to line n and they are each intersected by the same two transversals. Which angle is NOT necessarily congruent to 4? a. 12 b. 16 c. 7 d. 15 True or False: 93. If two parallel lines are intersected by a transversal, then alternate interior angles have measures of 90 degrees. 94. If two parallel lines are intersected by a transversal, then consecutive interior angles are supplementary. 10

Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1

Name: Class: Date: Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER Multiple Choice. Identify the choice that best completes the statement or answers the question.. Which statement(s) may