15. K is the midpoint of segment JL, JL = 4x - 2, and JK = 7. Find x, the length of KL, and JL. 8. two lines that do not intersect
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1 Name: Period Date Pre-AP Geometry Fall Semester Exam REVIEW *Chapter 1.1 Points Lines Planes Use the figure to name each of the following: 1. three non-collinear points 2. one line in three different ways 3. the intersection of the two planes 4. the intersection of the two lines 13. B is a point between points A and C, segment AC = 15.8, and segment AB = 9.9. Find the length of segment BC. (Draw a picture). Draw and label each of the following: 5. a segment with endpoints S and T with midpoint, M 14. Find the length of segment NP. 6. three coplanar lines that intersect in a common point 7. ray with endpoint F that passes through G 15. K is the midpoint of segment JL, JL = 4x - 2, and JK = 7. Find x, the length of KL, and JL. 8. two lines that do not intersect Use the figure to name each of the following: 9. a pair of opposite rays 10. the plane in two different ways *Chapter 1.2 Measuring Segments Find the length of the following: 11. Segment AB 12. Segment BC *Chapter 1.3 Measuring Angles 16. A is an acute angle. O is an obtuse angle. R is a right angle. Put A, O, and R in order from least to greatest by measure. 17. a. Which point is the vertex of BCD? b. Which rays form the sides of BCD?
2 18. Correctly name all 3 angles in the diagram *Chapter 1.4 Pairs of Angles Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent and and 4 Use the protractor to find the measure of each angle. Then classify each as acute, right, or obtuse and and 3 *Chapter 1.5 Using Formulas in Geometry 28. A rectangle has a length of (y 4) yards and a width of (y + 3) yards. a. Find the simplified perimeter in terms of y. 19. VXW 20. TXW 21. RXU b. Find the simplified area in terms of y. 22. L is in the interior of JKM, m JKL = 42, and m LKM = 28. Draw and label the diagram and use it to find m JKM. 29. Triangle B has the same area as Triangle A. Determine the height of Triangle B algebraically. 23. Ray BD bisects ABC, m ABD = (6x + 4), and m DBC = (8x - 4). Draw and label the diagram and use it to find m ABD. 30. The diameter of a circle is 4x 3 inches. a. Determine the simplified circumference of the circle in terms of π and x. b. Determine the simplified area of the circle in terms of π and x.
3 *Chapter 1.6 Midpoint, Distance, and the Pythagorean Theorem 31. Determine the length of the given triangle s hypotenuse. The answer should be given both rounded to the nearest tenth and in simplest radical form. Chapter 1.7 Transformations 35. A figure has vertices at G(0, 0), H(-1, -2), I(-1.5, 0), and J(-2.5, 2). Find the coordinates for the image of GHIJ after the translations that move the figure 2.5 units left and 4 units upward. 36. Below is the pre-image of ABCD. Identify the transformation from ABCD A B C D. 32. Y is the midpoint of XZ. X has coordinates (2, 4), and Y has coordinates ( 1, 1). Find the coordinates of Z. 33. Find the lengths below and leave your answer in simplest radical form. a. a. Find AB b. b. Find BC c. Find CA 34. TU has endpoints T(5a, -1b) and U(1a, -5b). Find the midpoint. c.
4 *Chapter 2.1 Inductive Reasoning 37. Inductive Reasoning is used to draw a conclusion from. 38. A statement you believe to be true based on Inductive Reasoning is called a. 39. To show that a conjecture is true, you must it. 40. To show that a conjecture is false, you can give a. 41. Complete each conjecture: a. A pair of complementary angles have a sum of. b. The square of any negative number is always. 42. Show that each conjecture is false by providing a counterexample: a. Two angles that have the same vertex are adjacent. 46. If 1 2 and 2 3, then If M is the midpoint of AB, then AM MB. 48. If AB = CD, then AB + EF = CD + EF and 2 form a linear pair, then they are supplementary. 50. If m A + m B = 90, then A and B are complementary. 51. If BX bisects ABC, then m ABX = m XBC. b. If x + 1 > 5, then x = 8 *Chapter 2.3 Deductive Reasoning 43. Deductive Reasoning is used to draw a conclusions from given,, and. *Chapter 2.5 Algebraic Proofs State which property, postulate, definition, or theorem supports each statement below. 44. If R is in the interior of PQS, then m PQR + m RQS = m PQS. 52. AB AB 53. If AM = MB, then AM MB. 54. If 1 and 2 are supplementary AND 2 and 3 are supplementary, then If X and Y are right angles, then X Y. 45. If 1 and 2 are supplementary, then m 1 + m 2 = 180.
5 56. Complete the following Algebraic Proof by listing each step and providing its justification. Write all possible answers for each of the following: 1. -2(x +5) = *Chapter 2.6 Geometric Proofs PRACTICE ANY AND ALL PROOFS!! Places to find proofs on Wroblewski s Website: *Writing Algebraic Proofs and Proof Practice 10/31 *Paragraph Proof Practice Theorems 11/17 *Proof Stations 11/19 *Test Review for Test 3 11/21 *Test 3 *Chapter 3.1 Lines and Angles Identify each of the following using the figure: 61. alternate interior angles 62. alternate exterior angles 63. corresponding angles 64. same-side interior angles Identify the type of angle pair given: (corresponding, alternate interior, alternate exterior, same side interior) 57. a pair of perpendicular segments 58. a pair of skew segments 59. a pair of parallel segments 60. a pair of parallel planes and and and and 4
6 *Chapter 3.2 Angles and Transversals 69. x = Find the coordinates of the midpoint of each segment: 80. AB with endpoints A (4, -6) and B (-4, 2) 70. x = 81. CD with endpoints C (0, -8) and D (3, 0) 71. Solve for x and find the missing angle: Use the Distance formula or Pythagorean theorem to find the length of each segment. Round answers to the nearest tenth. 82. Segment JK 72. Solve for x and find the missing angle: 83. Segment RS 84. Segment GF Use the figure to find the value of all the missing angles: 73. 1= 74. 2= 75. 3= 76. 4= 77. 5= 78. 6= 79. 7= 85. Find the slope of the given line. Say if it is positive, negative, zero or undefined.
7 Determine if the lines are parallel, perpendicular or neither by comparing their slopes x + 2y = 10 and y = -2x HJ: H (3, 2), J(4,1) 8. LM: L(-2, 2), M( 2, 5) KM: K (-2, -4), M(-1, -5) NP: N(0, 2), P(3, -2) Find the missing side for each triangle in simplest radical form AND as a decimal rounded to the nearest hundredth. Sketch and write the equation of the line that: 91. passes through (4, 7) and (-2, 1) in slopeintercept form passes through ( -4, 2) with slope ¾ in point-slope form. *Chapter 4.1 Classifying Triangles Determine whether the lines are parallel, intersect, or coincide. 93. y = -3x + 4 and y = -3x + 1 For problems , classify each triangle based upon its angle measures: 98. DFG 99. DEG 100. EFG 94. 6x - 12y = -24 and 3y = 2x + 18
8 For problems , classify each triangle based upon its side lengths: 101. EGF *Chapter 4.2 Angle Relationships in Triangles 102. DEF 103. DFG 104. Find the side lengths of the triangle: a Find m ABC 106. Find m ACD 107. Find m CAD 108. Find m L *Chapter 4.3 Congruent Triangles Identify the congruent corresponding parts: b Z 110. YZ 111. P 112. X 113. NQ 114. PN *Chapter SSS, SAS, ASA, AAS 115. Explain why the two triangles are congruent.
9 116. Show that the triangles are congruent when x = Given: AE CD and AE DC Prove: AEB DCB A C B E D 117. Use SSS, ASA, or AAS to determine if the triangles are congruent Determine if the triangles are congruent based upon the information given. Justify your answer. a Given: BD bisects ABC and AB BC Prove: ABD CBD B A D C b.
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