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Geometry Grade Level Fall Semester 2014 Final Examination Review Name_________________ Work each problem out. Completing the packet and showing work can get you up to five bonus points on the final exam. You must show your work and you may use a calculator. Round answers to the thousandths when needed. For Questions 1 – 24, match the definition on the right with the vocabulary term on the left. 1. 2. 3. 4. 5. 6. 7. ____ inequality ____ray ____vertex ____corresponding angles ____obtuse ____congruent ____bisector 8. ____regular 9. ____equilateral triangle 10. ____isosceles triangle 11. ____SSS 12. ____parallel lines 13. ____ASA 14. ____acute 15. ____equidistant 16. ____midpoint 17. ____scalene 18. ____ 60 19. ____segment 20. ____180 21. 22. 23. 24. ____plane ____hypothesis ____slope ____polygon a. the sum of the measures of all the angles in a triangle b. a triangle in which no sides are congruent c. the measure of each angle in an equilateral triangle d. the state of being unequal in quantity or measure e. a triangle with one angle greater than 90 f. coplanar lines which never intersect g. a postulate relating two angles and the included side of one triangle to the same for another triangle to show congruence h. being the same distance from two or more objects i. a point equidistant from the two endpoints of a segment j. a triangle in which all three sides are congruent k. the ratio of the rise of a line or line segment to its run l. a closed plane figure formed by three or more line segments m. having the same measure n. a part of a line that starts at an endpoint and extends forever in one direction o. a postulate relating three sides of one triangle to three sides of another to show congruence p. the part of a conditional statement containing the word if q. the part of a line containing two points and all the points in between them r. angles which lie on the same side of a transversal and on the same sides of the two intersected lines s. a triangle in which at least two sides are congruent t. a line, ray, or line segment which cuts an angle or line segment into equal parts u. a flat surface that has no thickness and extends forever v. a triangle with all angles less than 90 w. something both equilateral and equiangular x. the common endpoint of two sides of a polygon 25. A large facility for relief distribution during disasters is located at coordinates (12, 17) . An emergency occurs at (3, 12) . If the distance is measured in miles, estimate the number of miles it is from the facility to the place where the emergency occurred. _____ 26. TC has endpoints T (8, 13) and C (302,10.28) . Find the midpoint of TC . _____ 27. The measure of an angle is 28.1 . Find the measure of its complement and its supplement. complement_____ supplement_____ 28. Which angles shown form a vertical pair? a) G, Z c) J , O b) Z , P d) G, P Z V G P J B O e) G, V f) J , P 29. S is the midpoint of UA . US 14 x 5 units, and SA 20 x 37 units. Find the value of x and the length of SA . x _____ SA _____ 30. GAT and MAT are complementary. Find the measures of both angles if mGAT (14 x 12) and mMAT (6 x 28) . mGAT ________ mMAT ________ 31. Identify the hypothesis and conclusion of the conditional statement If Paul brings his guitar then we all sing. 32. Write the converse, the inverse, and the contrapositive of the conditional statement If she lives in Lubbock then she is a Texan. converse_________________________________________________________________________ inverse___________________________________________________________________________ contrapositive_____________________________________________________________________ 33. Which value of x provides a counterexample to the conjecture shown to prove that the conjecture is false? Conjecture: For any positive number x , a) x 5 10 x. x b) x 10 c) x 1 34. Write the following conditional statement as a biconditional. If an angle is a straight angle then its measure is 180 . ________________________________________________________________________________ 35. Help Mr. Juntti find the slope between the two points (16, 8) and (4,24) . _____ 36. Find the slope between the two points (2,18) and (2, 5) . _____ 37. Find the equation of the line with slope 10 passing through (3, 25) . 38. Coach Reed wanted to find out whether the lines given by y 2 parallel, perpendicular, or neither. Help him decide. __________ 1 x and y 12 3x are 3 _____ 39. Graph the line y 1 2 ( x 5) . 5 Use the illustration below for Questions 40 – 44. Lines U and L are parallel. T Y K N A R Z C U L F 40. Name a pair of vertical angles. _____ 41. Name a pair of same-side interior angles. _____ 42. Name the transversal. _____ 43. Name a pair of angles whose sum is 180 . _____ 44. If Z (5 x 12) and Y (7 x 6) , find the measure of Y . _____ 45. Find x in the triangle shown. _____ 11 (2 x 1) (6 x 13) 46. Which property allows you to show that the two triangles below are congruent? _____ 47. A decoration on the side of the Hyatt Hotel in Baton Rouge is in the shape of an isosceles triangle. If the two congruent angles in this triangle each measure 22.7 , what is the measure of the third angle? _____ 48. While experimenting with background designs for the spring play, Mrs. Prudhomme planned a triangular floor with all angles of equal measure. If she classified this triangle by its angle measure, what type of triangle would it be? _____ 49. Mr. Clayton had to cordon off the perimeter of the silo construction site below. What is the perimeter of the polygonal area shown? _____ 43 yds 54 yds 32 50. Given CAT PIG . This means that IP ________ . 51. A king built a small triangular playground for his daughters with each side twenty-seven meters long. What is the measure of each angle in this playground? _____ 52. Find the measure of J . _____ x (3x) 144 53. Compare the lengths of ET and BE . 29.1 30 m) ET BE J n) ET BE T o) ET BE B E 54. Find the length of PN . _____ 140 180 P N 180 140 220 55. Find the measure of LC given PH is the perpendicular bisector of LC . _____ H L 13 C 7 P 56. Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints (25,10) and (7,18) . __________ 57. Find UT . U _____ x 35 T 4 x 20 58. Mrs. Wolf’s large rectangular yard was 36 yards in length and 22 yards in width. Dogs constantly ran from one corner diagonally to the other. Find the length of the diagonal of the yard. _____ 59. Find the length of the hypotenuse of the triangle. _____ 60 ? 5 5 3 60. Which of the following would be a Pythagorean triple? a) 24, 7, 25 b) 1, 2, 3 c) 1, 1, 2 d) 6, 8, 10 61. If NAM 90 , find the length of NA . _____ A 43.8 in M N 45 62. A rectangular car lot has a length of 29 feet. The owner painted a stripe along the diagonal of the lot going from corner to corner; the diagonal stripe is 39.5 feet long. Find the width of the lot. _____ 63. Determine if the conjecture is valid or not valid by using the Law of Detachment. Given: If a student gets in a fight, then he is suspended. Raymond is suspended. Conjecture: Raymond was in a fight. _____ 64. Determine if the conjecture is valid or not valid by using the Law of Syllogism. Given: If Be’s ankle heals, she will join the girls track team. If she joins the girls track team, she will run the 400 meter relay. Conjecture: If Be’s ankle heals, she will run the 400 meter relay. _____ 65 and 66. Solve for x and y X = ____________ y= ________________ 67. Simplify the following to their simplest radical form. a) 98 b) 30 5 c) 64 d) 5.3 100 e) x32 f) 2x x 7 68. Find the value of x and the lengths of the missing sides in the triangle shown. Do the side lengths make a Pythagorean Triple? _____________________ 10 x 69. Given that and NP . x2 JKL MNP , KL 21x 2 , NP 20 x , LJ 15 x , and PM 13x 4 . Find x x ________ NP ________ 70. Find the perpendicular bisector in point-slope form for the line segment between the points (5,6) and (8, 4) . ________________________ 71. Write the point-slope equation y 7 3 ( x 20) in slope-intercept form. 4 __________ 72. Find the equation of the line containing (1, 11) and (4, 10) in slope-intercept form. __________ Study the material in this review packet, along with Chapters 1 – 5 of the book, your old notes, exams, and worksheets, and you will be prepared for the final examination!