/27 Intro to Geometry Review


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1 /27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the figure bisects FCB. If CG FCG = 9x + 3 and GCB = 13x9, find GCB and classify the type of angle. 4. A straight has a measure of. 5. Draw and label a plane Q. Put each of the following relationships in this plane. a. is in plane Q. AB b. intersects at P. ST AB c. Point X is collinear with points A and P. d. Point Y is not collinear with points T and P. e. Line contains points X and Y. The figure below refers to problems Line AD line CF, and m DOE= Find the length of BC. A 13cm B C 25cm 7. Find y if B is between A and C, AB is 2y, BC is 6y and AC is Find m EOF. 16. Find m AOB. 8. Find the complement of 40º. 9. Find the supplement of 150º comp 3 and 4 = 131. Find the measure of the rest of the angles of 2 complementary angles is twice the other. Find the measure of the angles. 11. One of 2 supplementary angles is 70 greater than the 2 nd. Find the measure of the larger angle. 12. If 2 angles are both supplementary and congruent, then they are. a. 1 = b. 2 = c. 3 = d. 5 = e. 6 = f. 7 = g. 8 = 1 Rev D.1
2 /32 Reasoning & Proofs Review 18. What are some things that can be assumed? c. d. 19. What are some things that cannot be assumed? c. d. 20. What are two things that can be concluded from Straight Angle? 21. What are two things that can be concluded from Right Angle? 22. What is one thing that can be concluded from Midpoint? 23. What is one thing that can be concluded from Bisect? For questions 2426, provide possible conclusions based on the diagram and given information. 24. Given: A is a right Conclusion: A D 25. Given: 3 sup to 4, 5 sup to 4 Conclusion: 26. Given: F sup G, H sup J, G J Conclusion: B C 27. Identify the hypothesis and conclusion of the following statement: If 2 lines are perpendicular then they form 4 right angles. 28. Write converse, inverse and contrapositive of If today is President s Day, then there is no school. a. Converse: b. Inverse: c. Contrapositive 29. Write the converse, inverse and contrapositive of a b a. Converse: b. Inverse: c. Contrapositive 30. Complete a truth table for r s (3pts) For problems 3135, state the property that justifies each statement. 31. AB AB 32. If A P then P A. XY PQ 33. If XY PQ then If 3( x 6) 0 then3x If a = b and b = c then a = c. 2 Rev D.1
3 /22 Lines in the Plane Review (Coordinates & Parallel Lines) 44. Identify the following pairings: 36. What is the slope formula? 37. What is the midpoint formula? 38. What is the distance formula? 39. Find the slope of the line that passes through (1, 3) and (5, 2) 40. Find the coordinates of the point where the median from A intersects BC. (4,3) B (6,5) A a. alternate interior: b. alternate exterior: c. corresponding: d. same side interior: e. same side exterior: 45. Given that m 14 51, find the value of the rest of the angles. C (6,1) 41. Given the following coordinate (2,3) perform the following transformations. a. reflect over xaxis b. reflect over yaxis c. translate to up 3 units 42. List 5 ways to prove lines. a. b. c. d. e. 43. Find x so that e f a. b. 46. Find m Rev D.1
4 /26 Triangle Properties Review 47. An acute triangle has 60. Find the value of x a. b. 48. An obtuse triangle has 49. A right triangle has 50. An equiangular triangle has 51. An equilateral triangle has 52. An isosceles triangle has 53. A scalene triangle has 54. A median is 55. An altitude is 56. Given YA is a median and XA x 6and ZA 2x 12 find ZX 61. Based on the diagram above, identify 5 angle relationships: a. b. c. d. e. 62. Name the longest side of ABC. 57. Determine whether the given measures can be lengths of the sides of a triangle: a. 2, 4, 5 b. 6, 9, Name the smallest angle of ABC. 58. Find the range for the measure of the third side of the triangle given the measures of 2 sides: a. 1 and 6 b. 82 and Determine the type of triangle, if any, based on the lengths of the 3 sides (Hint use Pythagorean Theorem): a. 8, 15, 17 b. 1, 1, Determine the relationship between the lengths of the sides AE and EB. 4 Rev D.1
5 /28 Triangles Review 65. What are some ways to prove 2 triangles are congruent? a. b. c. d. 66. What must you have in order to use the HL postulate? a. b. c. 71. Given the following indirect proof, what must be assumed? Given: AB AD, BAC DAC Prove: BC DC Complete the following proofs. 72. Given: FGI IGH, GI FH Prove: GIH is a right 67. Can CPCTC be used as a reason in a proof before proving any triangles are congruent? 68. When given a circle as a diagram, what can one assume? 69. Determine whether the pair of triangles is congruent. If so, write a congruence statement and explain why the triangles are congruent. a. b. Statements Reasons Given: C H, T is midpoint of AO Prove: CAT HOT Statements Reasons Indicate the needed information to make the 2 triangles congruent via AAS. 74. Given: HGJ KJG, KGJ HJG Prove: HG KJ Statements Reasons Rev D.1
6 /43 Polygons & Quadrilaterals 75. List 3 properties of a polygon. a. b. c. 76. Name the polygon based by its # of sides, convex/concave and regular/irregular. 77. List the properties of a parallelogram Beyond the properties of a parallelogram, list the properties of a rhombus. 79. Name all the properties of a kite. Which shapes also have these properties? 80. Name all the properties of a square. 81. List the properties of an isosceles trapezoid Name all quadrilaterals that have congruent opposite angles. a. b. c. d. 83. Name all quadrilaterals that have congruent diagonals. a. b. c. Use rhombus QRST for Questions If m QTS = 56, find m If m P = 6x, find x. 86. If TP = 15, find TR. Use rectangle ABCD for Questions If m DCE = 4x+5 and m DEC = 5x Find x. 88. If DC = 4x 30 and AB = 30x, find DC. 89. The bases of a trapezoid are 12 and 26. Find the length of the median. 90. Draw the quadrilateral tree representing the relationship of the various quadrilaterals. 6 Rev D.1
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