M2 GEOMETRY REVIEW FOR MIDTERM EXAM #1-11: True or false? If false, replace the underlined word or phrase to make a true sentence. 1. Two lines are perpendicular if they intersect to form a right angle. 2. Two angles are congruent if their measures have a sum of 90. 3. If two rays intersect at a common endpoint, a plane is formed. 4. A theorem is a statement that describes a fundamental relationship between the basic terms of geometry. For #5-7, refer to the figure at right. 5. 4 and 5 are corresponding angles. 6. Given r t, then consecutive interior angles 4 and 6 are supplementary. 7. Line p is a transversal since it intersects one or more lines in a plane at different points. 8. A triangle that is equilateral is also called a(n) acute triangle. 9. A(n) obtuse triangle has exactly one obtuse angle. 10. A reflection is a transformation that moves all points of a figure the same distance in the same direction. 11. When a figure can be folded so that the two halves match exactly, the fold is called a line of reflection. #12-17: Choose the correct term to complete each sentence. 12. Vertical angles are two (nonadjacent or collinear) angles formed by two intersecting lines. 13. The (midpoint or angle bisector) divides a line segment into two congruent segments. 14. When a linear equation is written in the form y = mx + b, m is the (transversal, slope) of the line and b is the y-intercept. 15. (Corresponding angles, Interior angles) are located between the lines cut by a transversal. 16. An (interior or exterior) angle is formed by one side of a triangle and the extension of another side. 17. The SAS Postulate involves two corresponding sides and the (exterior angle or included angle) they form. 1
#18-30: Use the vocabulary on your reference sheet to complete each sentence. 18. A(n)? divides an angle into two congruent angles. 19. Two angles are? if their measures have a sum of 180. 20. Two angles that lie in the same plane are called? if they share a common side and a common vertex. 21. The statement immediately following the word if is called the? of an if-then statement. 22. The statement immediately following the word then is called the? of an if-then statement. 23. The equation y 6 x 2 5 is in? form. 8 24. If two? are cut by a transversal, then each pair of alternate interior angles is congruent. 25. A(n)? organizes a series of statements in logical order, starting with the given statements. 26. A triangle that has one 90 angle is called a(n)?. 27. The ASA postulate involves two corresponding angles and their corresponding?. 28. The? is formed by the congruent legs of an isosceles triangle. 29. A transformation representing a flip of a figure is called a(n)?. 30. A(n)? is a transformation that turns every point of a pre-image through a specified angle and direction about a fixed point. #31-34: Use the figure at the right. 31. What is another name for line? 32. Name three points on plane P. 33. Name the intersection of planes P and N. 34. Name three non-coplanar points. 2
35. If the figure at right is not necessarily drawn to scale: a. State one thing we CAN assume from the diagram: b. State one thing we CANNOT assume from the diagram: 36. What is the length of AB? 37. Find the length of DE if D is between points C and E, CD = 6.5 cm, and CE = 13.8 cm. 38. Write an equation and solve. Then find the length of XZ shown at right. 39. A square has a side length of 2.3 ft. What is the area of the square? Include units with your answer. 40. A circle has a circumference of 6 cm. Find the diameter of the circle. Include units with your answer. #41-43: Use the coordinate grid given at right. 41. Find the distance between A and B. Express your answer in simplest radical form. 42. Find the coordinates of the midpoint of CD. 43. Find the coordinates of a point E if C is the midpoint of AE. 3
44. The vertices of a triangle are P 0,0, Q 8,6, and R 3,4. What is the perimeter of this triangle? 45. Find the value of x and y in the figure at right if UV bisects TW and UV = 40. 46. Use a protractor to measure PQR. Then classify PQR as right, acute, or obtuse. #47-48: In the figure, EA and EB are opposite rays, and EC bisects FEG. 47. Find the value of x if m FEG 82, and m FEC 5x 11. 48. If m AED 16y 10, find the value of y so that ED AB. 49. Find x, y, m 1, and m 2 in the figure at right. 4
#50-51: Use the polygons at the right. M2 GEOMETRY SEMESTER 1 REVIEW PACKET 50. Name polygon ABCDEF by its sides. Then classify it as convex or concave and regular or not regular. 51. Find the length of each side of polygon RST. 52. Two angles, 1 and 2, are supplementary. Angle 1 is an acute angle. What type of angle is 2? 53. Write an equation, and solve: The length of a rectangle is 3 more than twice its width. Find the area of the rectangle if its perimeter is 30 cm. 54. What is the perimeter of a regular hexagon if one side is 9 cm long? 55. Find the measure of one interior angle of a regular heptagon. 56. The measure of one exterior angle of a regular polygon is 15. How many sides does the polygon have? 57. Find the value of x in the figure at right. 58. Give a counterexample to show this statement is false: If XY = YZ, then Y is a midpoint of XZ. 5
59. Write the following statement in if-then form: All dogs have four feet. 60. Identify the hypothesis of the statement: If you live in Chicago, then you live in Illinois. 61. Write the converse of the statement: If two lines are perpendicular to the same line, then they are parallel. 62. Write the inverse of the statement: If today is January 1, then it is New Year s Day. 63. Write the contrapositive of the statement: If today is New Year s Day, then school is closed. 64. Complete the proof by supplying the missing information: 11 If 2x 7 4, then x. 2 Statements Reasons 1. 1. Given 2. 2x 7 7 4 7 3. 4. 2. 3. Simplify (or substitution) 4. 5. x 11 2 5. Simplify (or substitution) 65. If m 1 x 50 and m 2 3x 20, find m 1. 6
66. Complete the proof. Given: AC bisects Prove: 3 4 BAD. AC bisects BCD. 1 2 Statements 1. AC bisects BAD. AC bisects BCD. 1 2 2. and 3. 3 4 Reasons 1. Given 2. 3. #67-72: Give the reason that justifies each statement. 67. If M is the midpoint of AB, then AM MB. 68. If A B and B C, then A C. 69. If m A m B 90 and m B 20, then m A 20 90. 70. If X and Y are complementary, Z and Q are complementary, and X Z, then Y Q. 71. If PR QT, then PR = QT. 72. In the diagram at right, AB + BC = AC. #73-74: Refer to the figure at right. 73. Identify the intersection of plane SVX and plane STU. 74. Name a segment skew to WY. 7
#75-79: Refer to the figure at right. M2 GEOMETRY SEMESTER 1 REVIEW PACKET Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. 75. 2 and 12 76. 3 and 5 77. 7 and 15 78. If m n, and m 8 86, find m 13. 79. Find the values of x and y if m n, m 4 6x 5, m 10 5x 8, and m 9 3y 10. #80-82: Find the slope of the line that passes through the given points. Express answers as integers or fractions in simplest form. 80. V 10, 4, W 5,5 81. A 2,9, C 2, 15 82. G 6,14, L 3,9 #83-85: Find the slopes of CS and KP, and determine whether the lines are parallel, perpendicular, or neither. 83. C 1, 12, S 5,4, K 1,9, P 6, 6 84. C 5,6, S 3,2, K 2,10, P 1,4 85. C 6, 7, S 3, 5, K 3,3, P 9,7 8
#86-88: Write an equation for the line that satisfies the given conditions. 86. slope = 9, y-intercept = 3 87. slope = 3, contains ( 1, 5) 88. x-intercept is 3, y-intercept is 1 #89-91: Given the following information and the figure at right, determine which lines, if any, are parallel. State the reason that justifies your answer. 89. 1 2 90. DAB EBC 91. m ADE m BED 180 92. Find the value of x so that a b. 93. Use the grid to answer the following: a. Draw segment AB with A 1,8 and 5, 4 B. b. Find the midpoint M of AB. Label M on the graph. c. Find the slope of AB. d. Find the slope of a line perpendicular to AB. e. Write an equation for the perpendicular bisector of AB in point-slope form. f. Graph your equation from part (e) on the grid above. g. Use algebra to write your equation from part (e) in slope-intercept form. 9
94. Use a protractor and ruler to classify the triangle by its angles and sides. Round measurements to the nearest degree and nearest cm. 95. Find x, AB, BC, and AC if ABC is equilateral. 96. Use the distance formula to find the lengths of the sides of EFG if its vertices are E 3,3, 1, 1 G 3, 4. Then classify the triangle by its sides. F, and 97. Use the figure to find the measure of each numbered angle. 98. Write two different congruence statements for the triangles shown at right. #99-100: If the given postulate proves the two triangles are congruent, which additional parts of each pair of triangles should be shown congruent? 99. AAS 100. ASA P S D C R T Q A B 10
101. In the figure at right, IH bisects WIS. For each pair of triangles: (a) Are they congruent? (b) If yes, write the triangle congruency statement, and (c) give the postulate that makes them congruent. I a. Write a triangle congruence statement: W H S b. Explain why these two triangles are congruent. 102. Write a two column proof. Given: RS TS, and V is the midpoint of RT Prove: RSV TSV R V S T 103. Write a two column proof on separate paper. D Given: D F, and GE bisects DEF Prove: DG FG G E F 11
104. KLM is isosceles, and 1 2. a. Explain why LKP LMN. M2 GEOMETRY SEMESTER 1 REVIEW PACKET b. Name the reason that could be used to prove LKP LMN. Choose from SSS, SAS, ASA, and AAS. 105. Find m 1. 106. Find the value of x. 107. Write the coordinates of the image of P 2,5 reflected in the line y = 2. 108. Graph ABC with vertices A 4,4, B 3, 2, and C 1, 1 graph the image of ABC reflected in the y-axis.. Then 12
109. Graph the image of WX with W 7,1 and 110. Graph the image of AB with 3,1 X 4,5 after the translation x 4, y 3. 1,5 A and B after a rotation of 90 about the origin. 111. Find the coordinates of L if LMN with 112. ABC with vertices A 4, 4, 1, 2 L 3,1, M 1,6, and N 3,2 is rotated and 3, 1 90 about the origin and then reflected over the x-axis. B, C is rotated 180 about the origin. What are the coordinates of triangle A B C? 13