Geometry CP Semester 1 Review Packet. answers_december_2012.pdf


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1 Geometry CP Semester 1 Review Packet Name: *If you lose this packet, you may print off your teacher s webpage. If you can t find it on their webpage, you can find one here: answers_december_2012.pdf or use Additional Notes:
2 Geometry CP  Semester 1 Review Name: 1. Predict the next number. a. 1, 3, 7, 13, b. 500, 100, 20, 4, 2. In the diagram of collinear points, 3. Suppose J is between H and K. (draw a diagram) AB = BC = CD, AC = 10, and BE = 32. HJ = 4x 7, JK = 2x 3, and HK = 68. x = AB = DE = 4. Find the distance, slope, and midpoint between the points. a. (3, 7) and (7, 11) b. (1, 4) and (3, 9) distance = distance = midpoint = midpoint = slope = slope = HJ = JK = Is J the midpoint? 5. If m DBC = 72, 6. m ABD = (4x  1) find m ABD m DBC = (3x + 5) m ABC = 81 x = m ABD = m DBC = 7. m CBD = 35 m ABC = 113 List all the acceptable names for the angle m ABD = marked with one arc. 8. PT is an angle bisector of RPS. a. m TPS = 39 b. m RPT = (6x  17) m RPT = m TPS = (x + 28) m RPS = x = m RPS = 9. Use diagram below for each.. a. m 2 = 132 b. m 1 = (4x  3) m 3 = m 4 = (5x  6) m 4 = x = m 3 = c. m 1 = (3x + 32) d. m 1 = (10x  51) m 3 = (5x  12) m 2 = (2y) x = m 3 = (6x  11) m 1 = x = y =
3 10. Find the perimeter and area of each figure. a. b. Perimeter = Perimeter = Area = Area = 11. If the area of a rectangle is 84 square feet and the height is 7 feet, find the base. 12. If the area of a triangle is 48 square yards and the base is 6 yards, find the height. 13. If 4 and 5 are supplementary and m 4 = 19, find m The midpoint of a segment is (10, 16). One endpoint is (1, 8). Find the other endpoint. 15. Two angles are complementary, and one angle has a measure that is 9 times the measure of the other angle. What is the measure of the larger angle? 16. Use the diagram at the right. a. If m AFB = 68 o, what is the m EFG? b. If m AFB = 68 o, what is the m AFE? c. If GED is complementary to DEH and m GED = 46 o ; what is the m DEH? d. If FGC is supplementary to AFB and m AFB = 68 o ; what is the m FGC? e. If m EFG = 68 o, EFG FGE, and FGE GDE + 44 o ; what is the m GDE? f. If FEG is complementary to GED and GED is complementary to DEH, what is m FEG if m DEH = 44 o? g. If m CGD = 68 o and CGF BFG, what is m AFB? 17. Write the equation of a line that passes through (5, 7) and is parallel to y = 5x Find the equation of a line that passes through (5, 7) and is perpendicular to y = 5x + 2.
4 19. If AB CD, find x and y. 20. If AB CD and m 1 = 68 o, find m Find the values of the variables in each diagram. a. b. c. d. e. f. g. h.
5 22. Find the value of x that makes AB CD. a. b. 23. Supply the conclusion with a reason for each diagram and set of givens. a) GIVEN Conclusion Reason 1 and 2 are supp. 3 and 1 are supp. b) GIVEN Conclusion Reason m // n c) GIVEN Conclusion Reason 7 8 d) GIVEN Conclusion Reason RS SE e) GIVEN Conclusion Reason Diagram as shown 24. Rewrite the conditional statement in ifthen form. a. Supplementary angles have a sum of 180 o. b. Freshmen and sophomores are not allowed to drive to school. 25. Identify the hypothesis and the conclusion of each statement. a. Skew lines lie in different planes. b. I ll go to the game, if I don t have to work. hypothesis: hypothesis: conclusion: conclusion c. What is the negation of It is sunny?
6 26. Rewrite Vertical angles are congruent in conditional form and its converse. Conditional: Converse: Is the statement biconditional? If so, write in biconditional form. If not, give a counterexample. 27. Write a conclusion using the true statements. If no conclusion is possible, write no conclusion. If Al eats an apple, then Betty will buy a basketball. If Betty buys a basketball, the Charlie will eat cake. If Charlie eats cake, then Ditka will drive in the Daytona 500. Al is eating an Apple. Conclusion (if any): 28. Determine if the conclusion makes sense. If you practice, then you will remember all the lines. If you remember all the lines, you will get selected to be in the show. You got selected for the show; therefore you went to practice. True or False. Reasoning: 29. Use the given to determine which statements are true: Given:a // b Statements: a) 1 8 b) 1 is supp. to 3 c) 5 7 d) 6 is supp. to 7 e) 2 3 f) if t b, then b a g) 5 8 h) 3 and 7 are complementary 30. Classify the triangles by angles and by sides. a) b) c) angles: angles: angles: sides: sides: sides:
7 31. Find the value of x. a) b) 32. Solve to find the variables. a) b) c) d) e) f) 33. In ABC, m A = 54 o. The m B is 6 times the m C. Find the measure of each angle. (Draw a diagram) 34. In BFG, m F = 87 o. The m B is 7 times m G. Find the measure of each angle. (Draw a diagram) 35. In ABC, find x, and the measures of angles A, B and C. Also, classify ABC by its angles if m A = (5x 10)⁰, m B = (4x30)⁰, m C = 67⁰. (Draw a diagram.) 36. ABC DEF. Solve to find x and y. a) b) The perimeter of ABC is 41.
8 37. In the triangle, m C = 60 and m V = 59. Name the shortest side and the longest side. shortest side: longest side: 38. Given: KP is the bisector of RQ KP bisects RKQ LM = 18 NQ = 15, RP = 12 Find QR and MN. QR = MN = 39. The lengths of two sides of a triangle are given to be 21 meters and 17 meters long. Describe the possible lengths of the third side. 40. The measures of two sides of a triangle are given to be 9 feet and 10 feet long. Find a length of a segment whose measure would be too long to form a triangle with the given two measures. 41. Given: PW = 30, KD = 70, AD = Fill each blank with <, >, or =. find the perimeter of ΔHPW. a. AF DL b. WGP HGP 43. Write an inequality that compares QD to QZ. Then solve the inequality for x.(not drawn to scale.)
9 44. Write an inequality using the Hinge Theorem 45. In the diagram,hc is an angle bisector of (or converse) describing the restriction on x. ΔDHL. Solve for x and find DL. Then, solve it for x. 46. In the figure, TM is an altitude of ΔATJ. 47. Determine whether GR is a median of Find the value of x and AT. ΔNRP. Show work to justify your answer. 48. Given: AC is an altitude of ΔABE 49. Find the coordinates of the endpoints of the ΔABD is equilateral of the midsegment parallel to AC. AD is a median of ΔABE AB = 32 Find CE and m ADE. 50. Find the value of x and list the sides of ΔABC in order from shortest to longest if: m A 9x 29 m B 93 5x m C 10x 2 (Draw a diagram.) x = order of sides =
10 51. Given the diagram as marked. Find x and KM. 52. F, G, and E are midpoints of the sides of ΔBMY. If FG = 2x 1 and BY = 5x 7, find BE and BY. 53. Determine if each pair of triangles can be proved to be congruent. If so, state the reason. a) b) c) d) e) f) MD is a median MD is an altitude 54. What does CPCTC stand for and when is it used? 55. Give the name of any quadrilateral with the following characteristics: a) both pairs of opposite sides parallel b) one pair of opposite sides parallel c) opposite sides congruent d) opposite angles congruent e) all right angles f) all sides congruent d) Quadrilateral with all sides congruent and right angles. 56. List 5 properties of PARALLELOGRAMS Find the value of each variable in the parallelogram. 57c. Find m E. (not a parallelogram) a) b) c)
11 58. Find the missing lengths of the parallelogram: 59. Find the value of x that makes the JK = polygon a parallelogram. JM = MK = JL = 60. Find the value(s) of x that will make the polygon a parallelogram. a) b) 61. Find the value of each variable and the missing lengths in the parallelogram. a) b) x = HK x = y = Part 2. Proofs. You will need extra paper to complete most of the proofs. 1. Use coordinate geometry to verify LUKE is a parallelogram. Show all work and state the reason that proves the shape is a parallelogram. How do you know it is NOT a rectangle based on coordinate geometry? 2. Given: Wis a right angle 3. Given: O is the midpoint of DG S is a right angle Prove: DO OG Prove: W S
12 4. Given: Given: RS ST Prove: m // n WT ST Prove: S T 6. Given: Given: 5 8 Prove: 1 4 Prove: Given: BC EF 9. Given: C is the midpoint of BD BA ED AB // DE B E Prove: AB ED Prove: ABC DEF 10. Given: ID is an altitude of isosceles ΔVKI Prove: DV DK Statements 1. ID is an alt. of isos. ΔVKI IDV and IDK are rt. s IDV IDK ID ID V K VDI KDI Reasons 11. Use slope to determine which lines are perpendicular. Justify your reason.
13 1. a AB = 5 3. x = 13 4a. d = 2 29 b. d = 41 b. 4/5 DE = 22 HJ = 45 mid = (2,9) mid = (1,6.5) JK = 23 m = 2/5 m = 5/ ⁰ 6. x = m ABD= 78⁰ 8a. m RPT = 39⁰ b. x = 9 m ABD= 43⁰ m RPS = 78⁰ m RPS = 74⁰ m DBC= 38⁰, the angle can be named ABD or DBA 9a. m 3 = 48⁰ b. x = 21 c. x = 22 d. x = 10 10a. P = 28 b. P = 38 m 4 =132 m 3 =81 m 1 =98 y = 65.5 A = 40 A = a. 68⁰ 17. y = 5x a.x= 110⁰ y = 110⁰ 22a b. 112⁰ b. x = 115⁰ y = b ⁰ c. 44⁰ 18. y = 1/5x 8 c. x = 90⁰ y = 90⁰ 14. (21,24) d. 112⁰ d. x = 73⁰ y = 41⁰ ⁰ e. 24⁰ 19. x = 9, y = 54 e. x = 60⁰ y = 60⁰ f. 44⁰ f. x = 50⁰ y = 50⁰ g. 68⁰ 20. m 4 = 22⁰ g. x = 45 h. x = Conclusion Reason a. 1 3 If s are supp to the same, they are to each other. b. 5 supp 6 If // lines same side (consecutive) interior s are supplementary c. m // n If corresponding s are // lines d. S is the midpoint of RE If a point divides a segment into 2 segments it is a midpoint or S bisects RE If a point divides a segment into 2 segments it is bisected e. 1 4 or If s are vertical s 1 and 3 are a linear pair If s are adjacent and supplementary linear pair (assumed from diagram) 24a. If s are supplementary angles, then they have a sum of 180 o. b. If a student is a freshmen or a sophomore, then they are not allowed to drive to school. 25a. h: skew lines b. h: I don t have to work 26. If angles are vertical angles, then they are congruent. c: lie in different planes c: I ll go to the game If angles are congruent, then they are vertical angles. Negation: It is not sunny. Not biconditional because the converse is not true. 27. Ditka will drive in the Daytona a. right scalene 31a.70 o 28. False. You may be the only person that tried out. b. obtuse isosceles b. x = a, c, and d are true (rest are false) c. equilateral equiangular 32a. x = 76⁰ b. x = 8 or 5 c. x = 48⁰ d. x = 15 e. x = 16.4 f. x = 17 y= 23⁰, z = 132⁰ y = 84⁰ y = 40/3 y = 122⁰ 33. m A = 54 o 34. x = x = 17 36a. x = 23.7 b. x = short = LC m B = 108⁰ m F = 87⁰ m A = 75⁰ y = 17.8 y = 1 long = VC m C = 18⁰ m B = ⁰ m B = 38⁰ m G = ⁰ acute scalene 38. QR = < x < x > a. > b. > 43. 8x 5 > 7x + 2 MN = 18 x > x 3 > x = x = NG = 47 and PG = 73, not =, so RG is not a median. x > 8 DL = 92 AT = CE = (1,6) & (3,1) 50. x = x = x = 5, BE = 9, BY = 18 m ADE = 120⁰ AB, BC, AC KM = a. none 54. Corresponding 55a. parallelogram, rhombus, rectangle, square 56. opp. sides // b. SAS Parts of b. trapezoid, isosceles trapezoid opp. sides c. ASA Congruent c. parallelogram, rhombus, rectangle, square opp. s d. ASA or AAS Triangles are d. parallelogram, rhombus, rectangle, square consecutive s supp. e. SAS Congruent e. rectangle, square diagonals bisect each f. HL f. square, rhombus other g. square 57a. m = 133⁰ 58. JK = x = a. x = 4 or 1 61a. x = b. x = 16 n = 47⁰ JM = 52 60b. x = 2 or 5/4 HK = 29 y = 8 t = 78 MK = 62 b.x = 25, y = 24 c. 72 o JL = 90
14 1. Slope of LU and EK = 0/10. Same slope = parallel. Slope of LE and UK = 10/1. Same slope = parallel. However, slopes not opposite reciprocal, so not. Therefore, not a rectangle. 2. 1) W is a right angle 1) Given 2) S is a right angle 2) Given 3) W S 3) If 2 s are rt s they are 3. 1) O is the midpt of DG 1) Given 2) DO OG 2) If a pt. is a midpt. it splits a segment into 2 segments 4. 1) 2 3 1) Given 2) m // n 2) If alternate interior s are parallel lines 5. 1) RS ST 1) Given 2) WT ST 2) Given 3) S is a rt 3) if lines rt s 4) T is a rt 4) same as 3 5) S T 5) if s are rt s 6. 1) 2 3 1) Given 2) 3) 3 4 3) same as ) If s are vertical s 4) 1 4 4) transitive (if 2 s are to s they are to each other) 7. 1) 5 8 1) Given 2) 5 is supp to 1 2) If 2 s form a linear pair supp 3) 8 is supp to 4 3) same as 2 4) 1 4 4) Supplements of s are 8. 1) BC EF 1) Given 2) BA ED 2) Given 3) B E 3) Given 4) ABC DEF 4) SAS 9. 1) C is the midpt of BD 1) Given 2) BC CD 2) If a point is a midpoint it splits a segment into 2 segments 3) AB // ED 3) Given 4) A E 4) If // lines alternate interior angles 5) B D 5) same as 4 6) ABC EDC 6) AAS 7) AB ED 7) CPCTC 10. Reasons 1. Given 2. If a segment is an altitude then it forms right angles 3. If right angles, then congruent 4. Reflexive 5. If a triangle is isosceles, then the base angles are congruent 6. AAS 7. CPCTC *The missing statement for #7 is DV DK 11. Slope of AY = 8/3, slope of BD = 4/1, and slope of AB is 1/4, therefore BD AB because they have slopes that are opposite and reciprocal.
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