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Semester Exam Review Name________________ Period____ Honors Geometry 12-13 Classify each statement as always, sometimes or never true. 1. 2. 3. 4. 5. 6. Three points lie on exactly one line. Three points lie on exactly one plane. Two intersecting lines lie on exactly one plane. A line and a plane intersect in exactly one point. Three noncollinear points lie on two planes. Two planes intersect to form exactly one point. 7. DE and EF are opposite rays. 8. *Point E lies between D and F. DE= 2x 2 , EF 7 x , and DF = 4. Find the value of x. 9. * HB and HC trisect AHD . Such that mBHD mCHD Thus AHD is divided into 3 congruent angles. HD bisects BHE . If mBHC 32 , find mCHE . 10. *Let E be the midpoint of AC and E also be the midpoint of RS . AE=2x, EC = 16, RE = 2x+3y, and ES = x+26. Find the values of x and y. Provide a counterexample to show that each statement is false. 11. If D, E, and F are collinear, then DE + EF = DF. 12. If xy 5x , then y>5. 13. x 2 25 if and only if x = 5. 14. A figure is a rectangle if and only if it is a parallelogram. 15. An angle has a measure of 100 degrees if and only if it is an obtuse angle. 16. Write the converse of the following statement and determine if the converse is true or false. If BA=BC, then A is between B and C. 17. *A complement of an angle is four times as large as the angle. Find the measure of the angle. 18. *The measure of a supplement of an angle is 6 more than twice the measure of a complement of the angle. Find the measure of the angle. 19. *The coordinates of F and E are -4 and 16 respectively. C is the midpoint of ̅̅̅̅ and D is the midpoint of ̅̅̅̅ . Find FD. 20. *Find the values of x and y in the diagram at the right. (5y-20)° (x²+10)° 26° Use the picture at the right to determine which lines if any must be parallel based on the given information. a b e 21. _______ 2 5 2 1 5 6 7 22. _______ m4 m17 180 10 9 8 4 3 23. _______ m6 m7 m1 m13 24. _______ m17 m18 m10 17 18 19 22 21 20 16 13 15 14 c d Find the values of the variables in the pictures below. 25. * 70⁰ (2x-10)⁰ 26. * 27. * 40⁰ 5y⁰ 5y⁰ 2x⁰ 60⁰ (x-y)⁰ 71° y° 63° 28. *Find the sum of the measures of the interior angles of a convex heptagon. 29. *Find the measure of each interior angle of a regular dodecagon. 30. *The measure of each interior angle of a regular polygon is 6 times that of each exterior angle. How many sides does the polygon have? 31. *The vertices of ABC have coordinates A(-1,2), B(5,2), and C(1,5). Given G(5,3) and H(11,3), find all possible locations of I so that ABC GHI . Determine if the following triangles can be proved congruent. If so list the postulate that can be used. 32. 33. 34. 35. 60⁰ 60⁰ Find the value of x in the pictures below. 18⁰ 36. 37. 35⁰ x⁰ x⁰ 60⁰ 60⁰ 38. *Find the equation of the line in slope-intercept form that contains the altitude from A of the triangle with vertices of A(3,2), B(-1,6) and C(-5,-3). Put your answer in slope-intercept form if possible. 39. *Find the equation of the line in slope-intercept form that contains the median from C of the triangle with vertices of A(3,7), B(0,-2) and C(8,5). Put your answer in slope-intercept form if possible. 40. *Find the equation in slope-intercept form of the perpendicular bisector of AB given the triangle with vertices of A(-3,-5), B(4,-2) and C(5,5). Put your answer in slope-intercept form if possible. Determine if the following quadrilaterals can be proven to be parallelograms. If your answer is yes, provide the reason 41. 42. 43. Use the picture at the right to answer the following questions. 44. AC= 45. mBFD = C B 71⁰ 46. mCAE = 19 8D A 16 F 29 65⁰ E Write a two-column proof for the following. 47. Given: 1 2 , O is the midpoint of DB A 1 Prove: ABCD is a parallelogram B O 2 D 48. Given: AD BC; AD BC C D Prove: AB CD C 1 2 A B 49. Given: GK bisects JGI ; mH m1 Prove: J GK HI G H 2 1 K I 50. Given: m1 m2 C AD bisects CAB BD bisects CBA D Prove: m3 m4 A 1 3 4 2 B C 51. Given: A B; AD DB Prove: CD bisects ACB A Constructions: 52. Construct AB CD B A 53. Construct 1 2 1 D B 54. Construct the perpendicular bisector of AB B A 55. Construct line k through point P that is parallel to m. P m 56. Construct BD that bisects ABC . A B C