Geometry 1 st Semester review Name
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1 Geometry 1 st Semester review Name 1. What are the next three numbers in this sequence? 0, 3, 9, 18, For xercises 2 4, refer to the figure to the right. j k 2. Name the point(s) collinear to points H and I. Q R 3. Name all the point(s) coplanar to line j. L M G H I O F N J 4. Name three noncollinear points. K 5. Find F if = 23, F = 48, and is between and F. For xercises 6 7, refer to the given information and the figure below. 6. Find the length of. 7. Find the length of. Given: = 30, = 5, =, = 8. Point Y is between X and Z. Find the length of XY if XY = 5x + 2, YZ= 7x + 8, and XZ = Use points M(4, 2), N(4, 7), P(-1, 3) and Q(5, -2) to find each of the following. MN = PQ = NP = MQ =
2 For xercises 10 11, refer to the figure to the right. V W 10. Find m Ð WUY. 11. Find m Ð TUV. Given: m Ð VUW = 20 o m Ð YUX = 50 o m Ð XUW = 55 o 12. Find the midpoint of a segment with endpoints X(11, -5) and Y(8, -14). T U 13. bisects Ð. If m Ð = 63 o, what is m Ð? For xercises 14 16, refer to the figure to the right. V 14. Name two pairs of angles that form a linear pair? Which angles are supplementary? 15. Which angles are vertical angles? T If m Ð 1 = (6x 20) o, m Ð 5 = (7y + 12) o, and m Ð 4 = (3x + 7) o, Find the value of y. 17. Two angles are complementary. One angle has a measure that is twice the other angle. What is the measure of the smaller angle? 18. Two angles are supplementary. One angle is 5 times the other angle. What is the larger angle? 19. lassify the transformation as a rotation, reflection, or translation. a) b) 20. onsider the translation that is defined by the coordinate notation (x, y) (x 4, y+ 4). What are the coordinates of the image of each of the following: a) (2, -2) b) (-1, 3) c) (5, 7)
3 21. Sketch the image of (-2, 7) after a composition using the following transformations. a) Reflection: in the x-axis Rotation: 90 o clockwise about the origin b) Reflection: in the y-axis Translation: (x, y) (x 2, y 4) c) Rotation: 90 o clockwise about the origin Translation: (x, y) (x 5, y + 3) 22. What is the if-then form of group is a dozen if it has 12 objects? 23. What is the inverse of If it rains, then sidewalk is wet? 24. What is the contrapositive of If x = 7, then 3x + 3 = 24? 25. What is the biconditional form of the statement ll dogs bark? 26. Write each statement below as a biconditional statement, if possible a) If two lines do not intersect, then they are parallel. b) If two angles are complementary, then they add up to 90. c) If two angles are a linear pair, then they are supplementary. 27. Identify the conclusion that can be reached and tell which law of logic allows the conclusion to be made given the true statements #1 and #2 below? a) Statement #1: If two lines are perpendicular, then they form right angles. Statement #2: If two lines form right angles, then the angles are 90. onclusion:. Law of Logic b) Statement #1: If you study for the test, then you will get a good grade. Statement #2: rt studied for the test. onclusion: Law of Logic 28. Which property of equality matches each conditional statement: a) If x = 15, then x + 3 = 18. b) If x = 12, then 5x = 60 c) If x + y = 14, then 14 = x + y d) If x = n and n = 7, then x = 7
4 29. In the figure to the YZ. Find the length of XZ. 6x + 3 8x W X Y Z 30. Two angles, Ð 1 and Ð 2, are complementary. If m Ð 1 = 54 o, what is m Ð 2? 31. Use the figure to the right to find m Ð 2 if m Ð 1 = 41 o. 2 1 For xercises 32 33, refer to the figure to the right. 32. Find m Ð 2 if m Ð 3 = 115 o. 33. Solve for x if m Ð 4 = (4x + 5) o and m Ð 3 = (6x + 15) o For xercises 34 37, refer to the figure to the right. F G 34. and FG are. 35. Which lines are skew to? H 36. and H are. 37. Name a line parallel to G. For xercises 38 and 39, refer to the figure to the right. 38. Find the value of x. 39. Find the value of y. 41 y x 40. Use the figure below to determine the type angles shown and what is true when x y. z a) Ð1 and Ð3; Ð6 and Ð8 b) m Ð2 and mð3 1 x 2 c) m Ð1 and mð5 y d) m Ð2 and mð6 41. Use the figure to the right to determine which line segments are parallel. J M 5 80 I K L 45 N
5 42. Use the figure to the right to find the value of x that makes x y. x 110 y (4x + 30) 43. Which theorem or postulate proves a b in the figure to the right? c a b 44. Use the figure below to determine the value of x that makes a b. c 3x a (4x + 40) 45. Write the equation of the line has a y-intercept of 3 and is parallel to the line with equation y = x b 46. Identify each pair of lines as perpendicular, parallel, or neither? a) y = - x + 7; b) y = 7x + 3: c) y = - x 7 d) y = x y = x 7 y = 8x + 3 y = x 23 y x Given l m, m Ð 4 = 108 o and mð10 = 64, use the figure to the right to find the measure of each angle. 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 9 = 10 = 11 = 12 = 13 = 14 = 15 = 16 = l m p n
6 48. Find the slope of any line that is perpendicular to the line through (-2, 7) and (4, -11). 49. Use the figure to the right to find the value of x. 88 (4x + 10) 50. Use the figure to the right to find the value of x. 2x x Name the type of triangle described below. a) t least two congruent sides and an obtuse angle. b) three congruent sides. c) a right angle and two congruent sides. d) three acute angles and no congruent sides is. 8x Given ^, ^, which postulate or theorem can be used to 53. Find the measure of Ð1 in the figure to the right. 135 Ð1 54. n isosceles triangle has a perimeter of 64 cm. The lengths of the legs of the triangle are represented by (4x 5) and (7x 26). Find the length of the base of the triangle. For xercises 55 and 56, refer to the figure to the right. 55. Given Ð and Ð, find the value of x Find mð. 50 (5x + 30) F 57. In MNO and XYZ, MN@ XY and YZ. If the two triangles are congruent, what else must be true to prove the triangles congruent by SS?
7 58. Use the figure to the right to determine which postulate or theorem can be used to prove GHF? H F G 59. Given that Ð and Ð, what is the 3 rd congruence needed to prove F by S? 60. Tell which postulate or theorem can be used to prove that the triangles are congruent and give the congruence correspondence of the triangles? a) b) K L I J 61. What are the values of x and y in the figure at the right? 61 in in x 49 in y 62. What is the value of x in the figure to the right? x o 63. Find the m Ð in the figure to the right. m Ð = 30 o m Ð = (4x + 10) o m Ð = (6x + 20) o Use the figure to the right for xercises Given that F, G, and are the midpoints of KL, LM,and KM respectively, find FG. 4x - 5 F 6x + 2 L K G 65. Given that F, G, and are the midpoints of KL, LM,and KM respectively and m Ð KF = 62 o, find m Ð GFK. 14x - 8 M
8 8 66. In NPR, points O, Q, and S are midpoints of the sides. Find the slope and the length of OQ and NR in the figure to the right. N O S P Q R Using the figure to the right, list the sides in order from shortest to longest F -8 G 68. triangle has two sides that have lengths of 12 cm and 25 cm. Name two inequalities that could represent the length of the third side? 69. Tell if each set of measures will form a triangle? a) 2 cm, 3cm, 5 cm b) 20 in., 17 in., 40 in c) 8.3 ft., 4.3 ft., 4.9 ft. d) 12 cm, 12 cm, 1.5 cm e) 30.5 in., 58.5 in., 26.5 in. 70. In, mð = (3x + 25), mð = (7x 9), and mð = (2x + 20). List the sides of in order from shortest to longest. 71. Use the diagram below to complete the statement. a) If x = 27 and y = 26, then mð1 mð6. b) If mð1 = 100 and mð6 = 98 Then x y 1 20 in 19 in 3 2 x y in 20 in 6
9 72. Use the figure to the right to choose the inequality that correctly describes the restriction on the value of x. 22 m m x + 3 2x Use the figure to the right to find the length of NK when MN = 10 cm and MK = 24 cm. N M K
10 Geometry 1 st Semester Proof Review Name 1. Given:, Ð Prove: Ð 2. Given:, ^, ^ H 3. Given: HL and JK bisect each other. Prove: ÐH J M K L 4. Given: PW, QR@ WV Prove: PV P Q R v w
11 5. Given: PQ is an altitude and a median of OPR Prove: OPR is isosceles O R 6. Given: 3(2t + 9) = 30 Prove: t = ½ c d 7. Given: a b; c d Prove: Ð12 a b Given: Ð Prove: Ð
12 Geometry 1 st Semester Review Name: e able to define and understand all of the following terms and concepts. 1. onjecture 26. onditional Statements 2. Points 3. Lines 4. Planes 5. Segments 6. Rays 7. Length of a segment () 8. ollinear Points 9. oplanar Points 10. Opposite Rays 11. Intersection of two lines 12. Intersection of two planes 13. istance Formula 14. Midpoint Formula 15. etweenness of points 16. isect 17. Midpoint 18. Vertical ngles 19. Linear Pair 20. omplementary ngles 27. Hypothesis and onclusion 28. Inductive Reasoning 29. ounterexample 30. onverse 31. Inverse 32. ontrapositive 33. iconditional statement 34. Theorem 35. Law of etachment 36. Law of Syllogism 37. Perpendicular Lines 38. Line perpendicular to a plane 39. Parallel Lines 40. Parallel Planes 41. Transversal 42. lternate xterior ngles 43. lternate Interior ngles 44. orresponding ngles 45. onsecutive Interior ngles 21. Supplementary ngles 22. ngle ddition postulate 23. Segment ddition Postulate 24. ngles acute, right, obtuse 25. djacent ngles
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