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Name _______________________________________________ Date ___________________ Period ____ Geometry: Final Exam Study Guide For problems 1-3, find each numbered angle and give a reason for each answer. 1. 35 4 6. Given ABC with points A(-1, 5), B(-2, -3) and C(2, 3). The triangle is translated to form ABC where A is the point (4, 2). Find the point B 2 3 1 55 8. Given XYZ with points X(0, 2), Y(0, 5) and Z(-2, 4). The triangle is rotated 90 counterclockwise around the origin to form XYZ. Find the point Z. 2. 1 55 2 40 45 4 7. Given XYZ with points X(-3, 1), Y(1, 4) and Z(5, 2). The triangle is reflected across the x-axis to form XYZ. Find the point Z. 3 3. 13. Find x and y in the figure given M and N are midpoints. y M 78 N x 31 24 14. Find x and y in the figure given M and N are midpoints. 65 M 2x + 8 14 y N 40 9. Given XYZ with points X(4, 0), Y(8, 0) and Z(5, 3). The triangle is rotated 180 counterclockwise around the origin to 15. Find x in the rectangle form XYZ. Find the point Z. 2 x 10. Can the following set of three sides form a triangle? Yes or no. 85 3 a. b. c. 35 1 20 14, 20, 34 4, 19, 4 11, 5, 8 16. Find x in the rhombus. 4 4. Name the transformation shown in the figure below: x 11. Find the maximum and minimum values for the third side of a triangle with two sides given a. b. 25 60 and 62 14 and 20 12. List the three angles of the triangle in order from smallest to largest. 17. Find x and y in the parallelogram. 20 5. Given ABC with points A(1, 5), B(6, 3) and C(8, 7). The triangle is reflected across the y-axis to form ABC. Find the point B. Y 60 7 x 10 18 X 21 y Z Ebuen 1 of 4 Name _______________________________________________ Date ___________________ Period ____ Geometry: Final Exam Study Guide For problems 18-31, if the two triangles shown are congruent, give a reason (SSS, SAS, ASA, AAS, or HL) why they are congruent and write a correct congruence statement. If there is not enough information to say the triangles are congruent, write “not congruent”. 22. .27. D O K M G N E J 18. A B C 28. E 23. B E D A F C H G P 19. L F D 24. 29. X Y B Q 20. T R A Z C D X V W Y X Y 25. 30. A B W Z V 21. E D Z W 31. F 26. G X Y H H Z I K J W Ebuen 2 of 4 Name _______________________________________________ Date ___________________ Period ____ Geometry: Final Exam Study Guide 32. Find the sum of the measures of the exterior angles of a 20-gon. For problems 41-53, find x in each figure. 41. 48. 55 33. Find the measure of one exterior angle of a regular 15-gon 20 3x - 10 34. The measure of one interior angle of a regular polygon is 120. Find the number of sides of the polygon. 35. The measure of one exterior angle of a regular polygon is 40. Find the number of sides of the polygon. 33 x 49. 42. 9x x+5 36. Find x in the diagram below: x + 15 4x 50 50 50. x 75 50 70 80 2x + 10 40 60 43. 70 x + 30 51. 37. Find the sum of the measures of the interior angles of a hexagon. 38. Find the measure of one interior angle of a regular 15-gon x + 50 4x + 40 44. 25 4x 100 52. 39. The sum of the measures of the interior angles of a polygon is 3240. Find the number of sides of the polygon. x + 40 5x 5x + 20 40. Find x in each diagram below. a. x 45. 53. 100 30 25 2x + 50 x b. 120 x 4x - 30 130 x 100 80 Ebuen 3 of 4 Name _______________________________________________ Date ___________________ Period ____ Geometry: Final Exam Study Guide For problems 54-, find x in each figure. 54. 61. For each pair of points, find the midpoint and length of the segment connecting the points. a. (-3, 1) and (4, 4) b. (-1, 2) and (-7, -6) 3x + 22 5x - 2 55. 1 and 2 are complementary. m1 = 3x + 10 m2 = 2x Find x. For problems 62-63, use the Pythagorean Theorem to find the length of x. 62. 9 56. 12 x + 20 4x - 10 57. m AOC = 130 B x 63. 7 A 16 45 2x - 5 O C x 58. 1 and 2 are supplementary m1 = 3x m2 = x + 20 Find x. 59. Write the inverse, converse, and contrapositive of the conditional statement. Decide whether the converse is true or false. If false, provide a counterexample. a. b. c. If x = 12, then x2 = 144. If a number is odd, then it is divisible by three. If a figure is a square, then all of its angles are right angles. 60. Write an indirect proof to show that a triangle can have at most one obtuse angle. Ebuen 4 of 4