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Geometry 1st Semester Final Review 1. 7. M is the interior of TOP. If mTOM = 12.5 and mMOP = 16.5, then mTOP = . A plane is determined by …. 2. The three undefined terms in geometry are …. 3. If H is the midpoint of TE and TH = 11.22, then TE = . 4. What is the measure of C CE ? D 4x + 8 8. BD bisects ABC, m ABD = (7x – 1) , and m DBC = (4x + 8) . Find m ABD. 27 E 6x 9. Use inductive reasoning to determine the next three numbers in the following sequence: 1, -3, 5, -7, 9, … 5. Draw a plane with intersecting lines r and s and line s contains three collinear points A, B, C. 10. What three items are next in the pattern? 11. Evaluate 6. Solve: 2(4x – 3) –8 = 4 + 2x 3s 2 6r 2 , when s=5 and r=1 12. Use the distance formula to find BN. 17. Sketch a line that would have a zero slope. N y 7 6 5 18. Sketch a line that would have a undefined slope. 4 3 2 B 1 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 x –1 –2 –3 19. Write an equation of a line perpendicular to y= 1 x + 4? 2 –4 –5 –6 –7 20. What is the equation of the line though (-1, 7) and (4, -3)? 13. Given GH with endpoints G(-6, -6) and H(1, 2), what are the coordinates of the midpoint? 21. Write an equation of a line parallel to y= 14. What is the slope of the line through (7, 6) and (3, -2)? 15. Sketch a line that would have a negative slope. 16. Sketch a line that would have a positive slope. 1 x + 2? 2 22. Determine whether the pair of lines 12x + 3y = 3 and y = 4x + 1 are parallel, intersect, or coincide. 26. Find the measure of the supplement of R, where m R = 132.6 23. l1 || l2, then … 27. Identify the hypothesis and the conclusion of the conditional statement. If it is raining, then the sun is not shining. H: which angles are corresponding angles and what is their property? C: 28. Write the logic symbolism for; conditional statement: which angles are alternate interior angles and what is their property? converse statement: inverse statement: which angles are same side interior angles and what is their property? contrapositive statement: biconditional statement: law of syllogism: 24. l1 || l2, find m1, if the m2 = 6x + 26, and m4 = 2x + 10. 29. Simplify the following ( a - e ): a) b) c) d) 25. Find the measure of the complement of M, where m M = 32.6 125 98 3 2 72 e) ( 5) 2 30. Write the converse, inverse, and contrapositive of the conditional statement: If it is a horse, then it has 4 legs. 33. ∆ABC is an isosceles triangle. AB is the shortest side with length 3x + 9. BC = 8x – 8 and CA = 3x + 27. Find AB. converse statement: inverse statement: 34. One of the acute angles in a right triangle has a measure of 41.7°. What is the measure of the other contrapositive statement: 31. Classify ∆DAB by its angle measures, given mDAB = 56 and mABD = 72 . 32. Classify ∆DBC by its angle measures, given mBDC = 26 and mDCB = 51 . acute angle? 35. Given that ∆ABC ∆DEC and mE = 47º, find mACB. 36. What is the m CBA, if m CAB = 26? 37. What is the value of x, if m CBA = 6x? 38. What is the mACD, if mABC = 37 ? 39. AB = 16.5, AX = 7.9, and BC = 16.5. What is the length of 44. Write a congruence statement for these triangles, and name the postulate or theorem that supports it. AC ? 45. What can you use to prove ABE CDE. 40. The circumcenter is equidistant from the of a triangle? 46. Classify HG and EF . 41. The orthocenter of a triangle is the point of concurrency of which lines? 42. The incenter is equidistant from the of a triangle? 47. Given: x? TUV TWV. What is the value of 43. Write a congruence statement for these triangles, and name the postulate or theorem that supports it. 48. List the sides of to longest? ABC in order from shortest B 75 A 50 55 C 49. . List the angles of smallest to largest? GHJ in order from 54. Given that YW bisects XYZ and WZ = 14.3, find WX. 50. Find the measure of ‘x’. 55. Tell whether a triangle can have sides with lengths 4, 2, and 7. 122 56. HK and x JK are angle bisectors of ∆JHI. 51. Find the measure of ‘x’. 3x - 17 Find m HIJ . 2x - 5 x + 40 57. HK and JK are angle bisectors of ∆JHI. 52. Find the measure of BCA. Find the distance from K to 58. 53. In ∆ABC, ZC, YB, and XA are the medians of the triangle. BY = 6.6, find BO. C X Y O B Z A JI . What is the orthocenter of this triangle? 59. Find the values of x and y. Express your answers in simplest radical form. 64. Find the two missing side lengths. 30 60 8 60. Find the value of x. Express your answer in simplest radical form. 65. Find the missing side. 4 61. . The vertices of square ABCD are the midpoints of the sides of a larger square. Find the perimeter and the area of square ABCD. Round to the nearest hundredth. 5 66. A painter leans a 15 foot ladder against a house. The base of the ladder is 5 feet from the house. To the nearest tenth of a foot, how high on the house does the ladder reach? ABC with AB = 22, find the length of midsegment XY . 62. Given 67. Find the length of each leg. 12 45 63. Find the two missing side lengths. 68. Find the missing side lengths. 5 3 60 30 3 2 45