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Transcript
ADVANCED GEOMETRY: FALL 2016 SEMESTER REVIEW On a separate sheet of paper, write a two-column algebra proof for the following problems. 1. Given: 3x + 12 = 8x – 18 Prove: x = 6 2. Given: 3(5x + 1) = 13x + 5 Prove: x = 1 3. Given: 6( x 4) 3 5 x 30 2 x Prove: x 3 Fill in the correct term to complete each sentence. 4) 5) 6) 7) 8) 9) 10) 11) Two angles whose sum is 90 are _____________. An angle that measures 120 is an _____________ angle. Two angles whose measures have a sum of 180 are ___________. Opposite rays form a ____________ and share an ____________. The intersection of two planes is a ________________. Adjacent angles share a _____________. Vertical angles are ______________. A segment bisector divides a segment into two _____ segments. I. State whether each Postulate or Conjecture is TRUE (A) or FALSE (B). _______________12) A plane contains at least 3 points all on the same line. _______________13) A part of a line that consists of two points called endpoints, and all the points between them can be termed a segment. _______________14) Any plane can also be identified by a lower case script letter in the middle of the plane. 15) Find the best counterexample to show that the following conjecture is false: “Any three points that are coplanar are also collinear.” A A, C, and F are coplanar but not collinear. B A, E, and F are coplanar but not collinear. C A, B, and D are collinear but not coplanar. 16) Which is not an example of deductive reasoning? 17) Which statement does not have a true contrapositive? A Coach Moyer is 25, therefore next year she will be 26. A If a polygon is a square, then it is a quadrilateral. B If Filipe does this review, then he will pass. C Acute angles are less than 90 degrees. A is 40 degrees, then A is acute. If B If a vehicle has four wheels, then it is a car. C If the sum of the measures of two angles is 90 , then the angles are complementary. 18. Turtles don’t fly. If-Then: __________________________________________________________T or F Counterexample? ___________________________________ Converse: _________________________________________________________T or F Counterexample? ___________________________________ Inverse: __________________________________________________________T or F Counterexample? ___________________________________ Contrapositive: _____________________________________________________T or F Counterexample?__________________________________ State the law used (Law of Detachment or Law of Syllogism). Write the conclusion. 19. If Miss Hays worked for the Astros, then she would give all of her students free tickets. Miss Hays works for the Astros. Law: _________________ Conclusion: __________________________________________________________ 20. If Mrs Lucas is in a meeting, then you can’t go to tutorials. If you can’t go to tutorials, then you will fail this exam. Law: __________________ Conclusion: __________________________________________________________ 21. Find mC if C D, mC = 3x – 5, and mD = 2x + 5. A. 36 B. 35 C. 20 D. 25 22. Find m1. A. 35 C. 145 (4 1 (6 x x+ 1 3) 3) D A B B. 165 D. 15 23. If mABD = 45 and mABC = 120, find mDBC. A. 120 B. 75 C. 70 D. 80 24. If EB bisects AED and mDEB = 61, find mAED A. 90 B. 180 C. 30 D. 122 B A C C D E 25. In which diagram(s) are 1 and 2 supplementary? I IV 12 A. B. C. D. I only II only II and IV I, III, and IV 12 12 II 1 2 III 1 26. If m1 = 7x – 5 and m2 = 5x + 27, what is the value of x? A. 16 B. 32 C. 107 D. 73 27. 4 and 5 form a linear pair and m4 = 62. Find m5. A. 62 B. 28 C. 118 D. 90 1 2 28. Given: B is the midpoint of AC . Prove: BD BC BD AB Statements 1. Reasons BD AB 1. ___________________________ 2. B is the midpoint of AC 2. ___________________________ 3. AB BC 3. ___________________________ 4. BD BC 4. ___________________________ 30. a. Show 2 different ways on how congruent segments can be formed using a compass: b. What does your teacher need to see in order to accept it as a correct answer? c. Can you assume anything to be congruent? From the figure on the right, match the angle pairs with their correct name. 31. _________ ∠1 and ∠8 a. Same Side Interior 32. _________ ∠3 and ∠5 b. Corresponding 33. _________ ∠2 and ∠8 c. Alternate Exterior 34. _________ ∠4 and ∠5 d. Alternate Interior 35. _________ ∠3 and ∠7 e. Same Side Exterior 36. Use the diagram to answer the question. Which statement proves that g || h? A) 1 4 B) m5 + m7 = 180˚ C) 1 6 D) m2 + m8 = 180˚ 37. Given the diagram, which statement and reason can be used to prove b || c? a b c 14 23 57 68 A) 2 7, Alternate Exterior Angles Theorem B) 2 6, Same Side Interior Angles Theorem C) 1 4, Linear Pair Postulate D) 1 3, Vertical Angles Theorem Use the figure at the right for the next 4 questions. l 38. Identify the special angle pair name for 10 and 6. A. alternate interior B. vertical C. corresponding D. alternate exterior 87 1 56 1029 1 34 1 39. Given l m and m5 = 72, find m10. A. 108 B. 72 C. 18 D. 112 40. Given lm , m11 = 9x + 5, and m3 = x + 37, find the value of x. A. 32 B. 4 C. 41 D. 5 41. Given m8 = 5x - 2 and m9 = 3x + 70, find the value of x so that l m. A. 16 B. 14 C. 62 D. 75 a 42. Find the value of x so that m n A. 12 B. 20 C. 35 D. 40 1 1 7 b 3 x 4 + 18 2 m n m p Refer to the graph below to find each measure. If the measure is not a whole number, round to the nearest hundredth. 43) Find the distance between H and L. __________. 44) What is the distance between J and H? __________. 45) What is the measure of segment IN? ____________. 46) Find the midpoint of NJ. ____________. 47) F is the midpoint of EG. If EF = 2x + 3 and EG = 6x - 3, find FG.____________. Find the slope of a line parallel AND perpendicular to the line passing through the given points. 48) A (4, 1), B (2, 0) ______________ _____________ 49) C (2, -1), D (4, 2) ______________ _____________ 50. Name the equation of the line whose slope = 5 , and y-intercept = 3/2? A. y = ¾x – 3/2 B. y –2 = 5(x – 3) C. y = 3/2x – 5 D. y = 5x + 3/2 51. Name the equation of the line through the points (2, 10) and (-2, 2) A. y = 2x +10 B. y = ½ x +9 C. y = ½ x +10 D. y = 2x + 6 52. Name the slope of the line y + 3 = -½(x - 1). A. ½ B. –1/3 C. -½ 53. Which of the following is the graph of y = 2x + 3? A. B. D. 3/1 C. D. 54. Find the value of x. The diagram is not to scale. 114° 45° x° A. 21 55. B. 66 C. 45 D. 31 Find the value of x. The diagram is not to scale. 45 x 45 35 24 24 A. 90 B. 48 C. 35 D. 70 56. Which three lengths could be the lengths of the sides of a triangle? A. 12 cm, 5 cm, 17 cm C. 9 cm, 15 cm, 23 cm B. 21 cm, 5 cm, 7 cm D. 6 cm, 22 cm, 11 cm 57. Points B, D, and F are midpoints of the sides of The diagram is not to scale. EC = 30 and DF = 17. Find AC. A B F C E A. 30 D B. 8.5 C. 60 D. 34 58. Find the value of x. 14 2x – 9 A. 10 59. B. 8 C. 7 Name the smallest angle of D. 11.5 The diagram is not to scale. C 8 9 7 A B A. B. 60. C. D. Two angles are the same size and smaller than the third. What is the value of x? 32° 21 21 xº Drawing not to scale A. 158° B. 148° C. 74° D. 79° 61. List the sides in order from shortest to longest. The diagram is not to scale. J 71° 84° K 25° L A. B. C. D. Matching For the next 5 questions, choose the Letter that matches the definition A. Equilateral Triangle D. Median B. Isosceles Triangle E. Altitude C. Scalene Triangle ____ 62. A triangle with two sides congruent and base angles congruent ____ 63. A segment that connects a vertex of triangle with the midpoint of the opposite side ____ 64. A triangle with all sides congruent and all angles congruent ____ 65. A segment that connects a vertex of a triangle with the opposite side and is perpendicular to the opposite ____ 66. A triangle with no sides congruent ____ 67. Name a median for | A E ) | D ) C A. F B B. C. D. ____ 68. Two sides of a triangle have lengths 5 and 12. Which inequalities represent the possible lengths for the third side, x? A. C. B. D. Matching For the next 5 questions, match the letter to the correct definition A. Orthocenter D. Circumcenter B. Incenter E. Midsegment C. Centroid ____ 69. The point of concurrency of Altitudes of a triangle ____ 100. A segment that connects the midpoints of two sides of a triangle ____ 101. The point of concurrency of Medians of a triangle ____ 102. The point of concurrency of Perpendicular Bisecters of a triangle ____ 103. The point of concurrency of Angle Bisectors of a triangle 104. The coordinates of the image of ABC after a reflection over the y-axis are: A. A(5,-1), B(4,-7), C(1,-3) B. A(-5,1), B(-4,7), C(-1,3) C. A(-1,-5), B(-7,-4), C(-3,-1) D. A(-1,5), B(-7,4), C(-3,1) B C A 105. A transformation is described in the equation (x,y) = (3x, ½y). Which of the following best describes what the transformation does to the geometric figure? A. enlargement B. reduction C. horizontal stretch and vertical shrink D. horizontal shrink and vertical stretch 106. The coordinates of the image of quadrilateral DEFG after a D slide of 2 units up and 3 units left are: A. D(4,2), E(6,-2), F(0,-8), G(-2,-4) E G B. D(0,8), E(2,4), F(-4,-2), G(-2,-2) F C. D(5,3), E(7,-1), F(1,-7), G(-1,-3) D. D(-1,7), E(1,3), F(-5,-3), G(-7,1) 107. Find the coordinates of the image of the point with coordinates (3,6) after a rotation of 270 A. (6,-3) B. (-6,3) C. (–3,-6) D. (3,-6) 108. Which of the following transformations would preserve the slopes of lines? I. Translations II. 180 rotation III. Dilation IV. Reflection over the y-axis V. Distortion A. I, IV, and V B. II and III C. I, II, and III D. I - V GIVEN: Similar Trapezoids ABCD and EFGH: B 4 C F G H 5 2 6 A E 8 D 109) a) What is the ratio of the perimeters of the trapezoids shown? __________________ b) Find the perimeter of trapezoid GHEF. __________________ B Given ABC ~ EFG, solve the following problems. F A C E G 110) If the perimeter of ABC is 36, the perimeter of EFG is 12, given that BC is 12, find the measure of FG. __________________. 111. If BCDE is congruent to OPQR, then is congruent to ________. A. B. 112. Given A. 22 C. and B. 11 , find C. 10 D. and D. 25 113. Is there enough information to prove the pair of triangles congruent? If so, state the postulate or theorem you would use to prove that the triangles are congruent. A. Not enough information B. AAS C. SAS D. HL 114. Given the figure, SAC ___________ C Y A A) A Y R B) Y R A C) RAY D) Y A R R S 115. What additional information is needed to prove PQR PTR by the HL Theorem? A) Q T B) QR RT C) Q P R T P R D) QP TP P Q R T 116. Given the figure, which theorem or postulate proves the triangles congruent? A) ASA B) AAS C) SSS D) SAS 117. With the figure to the right, CSK JKS and CS JK . Complete the following congruency statement and provide the theorem why it which theorem or postulate that proves the triangles congruent? SKC __________ by __________ K S A) C) K S J b y S S S J K S b y A S A B) D) KSJ by SAS C J J K S b y S A S 118. Given the figure, what postulate or theorem proves the right triangles congruent? A) HL B) LL C) HA D) LA 119. Given EDH GFH , what additional information is needed to prove DHE FHG by the ASA postulate? D E H G A) G H H E B) DE FG C) G E F D D) F H D H 120. What are the three undefined terms? _______________________________ F