Geometry CP Midterm Exam Review Name Teacher
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- Verity McCoy
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1 Name Teacher Review Packet: 1. The format of the review packet is not the format of the exam. 2. Please refer back to previous notes, homework, and class examples for more practice. 3. omplete the packet to the best of your ability on your own, then bring your remaining questions to us. Exam Helpful Hints: 1. Read directions very carefully. 2. When necessary, draw a diagram! 3. Use the choices of multiple choice questions. Exam Info: 1. Format: The exam will include multiple choice as well as open-ended questions. 2. Students will be allowed to use calculators (graphing calculators will be required to clear all memory!) You MUST bring your own! You will not be provided with one. 3. If you are found with any materials regarding this exam, or in your calculator, you will fail the exam with a ZERO. 4. No ell phones are permitted in the exam area. Leave them at home or in your lockers. 1
2 Vocabulary: You are responsible for the following terms, theorems and postulates. collinear Points coplanar Points ray plane line line Segment segment addition postulate segement subtraction postulate midpoint bisect acute angle right angle obtuse angle straight angle angle bisector complementary angles Parallel Lines Perpendicular Lines Skew Lines Parallel Planes Perpendicular Planes orresponding angles a. Postulate b. onverse lternate interior angles a. Theorem b. onverse lternate exterior angles a. Theorem b. onverse onsecutive interior angles a. Theorem b. onverse Right Triangle Scalene Triangle Equilateral Triangle Equiangular Triangle cute Triangle Isosceles Triangle Obtuse Triangle Exterior ngle Theorem ase ngles Theorem a. onverse Hinge Theorem a. onverse Triangle Inequality Theorem Perimeter rea of Triangle Midsegment supplementary angles adjacent angles linear pair vertical angles linear pair postulate vertical angle theorem polygon equilateral equiangular regular polygon concave polygon convex polygon interior angles exterior angles conditional converse inverse contrapositive SSS SS HL S S a. Theorem Perpendicular isector a. Theorem b. onverse Median ltitude 2
3 Points, lines and planes For questions 1-9, use the diagram to determine if the statement is true or false. 1. & GEare parallel 2. & D are perpendicular 3. GE& HDare skew K J 4., J, and are collinear H G D 5., G, and E are collinear 6., J, H, and G are coplanar 7., G, H and D are coplanar 8. K is between and 9. There are no parallel planes in this diagram. ngles 10. Use the diagram. Find the value of x and m 1. (4x + 3) 1 (6x - 22) F 11. Use the diagram. bisects PT, m QT = 5x 5 and m PQ = x Find the value of x, and the m PT. E P Q S T 12. Two angles are supplementary. One angle is 5 less than 4 times the other. Find the measure of each angle. 13. Two angles are complementary. One angle is 4 times the other. Find the measure of the larger angle. 3
4 For questions 14-19, use the diagram. Given that X and D D, identify each of the following. 14. right angle 15. Two congruent supplementary angles 16. Two non-congruent supplementary angles 17. Two adjacent complementary angles 18. pair of vertical angles 19. midpoint 20. In the figure below bisects D and bisects E. EF = 4x + 7, F = 7x 20 a) Solve for x. D E F b) Determine the measure of D. 21. In the figure below, D = x + 7, DE = 2x 20, E = 70. a) Solve for x. D E F b) Determine the measure of D. 4
5 Segment and Line Properties 22. K is a point between and. = 3x, = 2x + 8, and = x 5. What is the length of? 23. H is the midpoint of. = 18 and = 3x + 2. Find the length of? 24. In the diagram, is the midpoint of and D is the midpoint of. = 4x-3 = 12x + 26 D a) Solve for x. b) What is the length of? 25. What is the distance between the points (4,-2) & (2,-1) 26. What is the midpoint of the segment that connects the points (4,6) & (0,-4) 27. In segment, M is the midpoint. Given (2,3) and M(5,7), find the coordinates of endpoint. 28. What is the slope of the line passing through the points (-8,1) & (-5,-8)? 5
6 29. What is the slope of a line that is to a line with slope 3? What is the slope of a line that is to a line that has a slope 3? 31. K is a point between and. = 3x, = 2x + 8, = x 5. a) Solve for x. b) Is K the midpoint of? Parallel Lines For questions 37-43, use the diagram to determine which lines, if any, are parallel based on the given statement P is supplementary to Q is supplementary to X. 37. Z P For questions 39-43, use the diagram which shows two sets of parallel lines. 39. If m 1 = 100, find m If m 9 = 120, find m If m 2 = 62, find m If 7 = (5x + 8), 14 = (12x + 2), solve for x. Z W 43. If 6 = (8x + 5), 10 = (10x - 7), solve for x. Q P 5 Y X S R 6
7 Logic For questions 44-48, use the conditional statement If two angles are vertical, then they are congruent. 44. Write the converse: 45. Write the inverse: 46. Write the contrapositive: 47. an this be written as a biconditional statement? 48. Since the conditional statement is true, which other statement is also true? Triangles 49. The exterior angle at the base of an isosceles triangle measures 130. Find the measure of the vertex angle. 50. In, m = 40, m = 70 and = 5. Find. 51. The three angles of a triangle are (x + 30), (4x + 30) and (10x 30). Find the value of the smallest angle. 52. QRS is isosceles with Q S. If = x + 16, = 3x 30 and = 2x 20. Find the length of the base. 7
8 53. In, m = 30 and m = 70. What is the largest side of the triangle? 54. In equilateral R, point P is the midpoint of, and point E is the midpoint of. If = 8, what is the perimeter of R. 55. In GHI, m H is 20 more than m G and m G is 8 more than m I. What is the measure of each angle? 56. If a triangle has sides length 5 and 8, what are the possibilities for the length of the third side? For questions 45-48, use the diagram. 57. m 1 = 40, m 2 = 110, m 5 = 58. m 1 = 55, m 2 = 95, m 6 = 59. m 4 = 118, m 1 = (2x + 8), m 3 = (x + 5). x = m 1 = (3x +12), m 2 = (2x + 14), m 3 = (8x 15). x = 8
9 For questions 61-78, use the diagram. 61. QVP QRT 67. QVS 68. What type of triangle is PVT? 69. If m 1 = 30, m PVT = 70. PVQ PQT m 3 + = If m 3 = 95, m 6 =. 78. What type of triangle is PTR? For questions 79-83, use the diagram to determine which method, if any, proves the triangles congruent. 79. is a median, , , 82. is the midpoint of , D For questions 84-86, name the postulate that proves the triangles are congruent
10 For questions 87-90, use with coordinates (1,7), (5,2), (0,-2). 87. Draw the triangle. 88. Find the slopes of each side. 89. Find the length of each side. 90. Prove that triangle is an isosceles right triangle. Proofs Write a complete proof (paragraph or two-column) 91. Given: is the midpoint of, Prove: 92. Given: bisects bisects Prove: 10
11 93. Use the diagram to solve for x and y. Round to the nearest tenth. 94. Use the diagram to solve for x and y. 5y+10 7x 12x+6 3y+1 For questions , determine if the statement is always, sometimes, or never true. 95. If a triangle is isosceles it is also equilateral 96. is a rule used to prove two triangles congruent. 97. If two angles are congruent, then they are vertical. 98. ngles that form a linear pair are complementary 99. In triangle, if point D is the midpoint of, then D is a median of the triangle If alternate exterior angles are supplementary, then the lines are // n equilateral triangle is isosceles n acute triangle is right n acute triangle is isosceles right triangle is scalene n altitude of a triangle can be outside the triangle n angle bisector of a triangle is also the median of the triangle. 11
12 Special Segments in Triangles In the diagram, is an altitude of. = x + 7, = 2x 15 and m D = (4x 6). Solve for x. D 108. In the diagram, is a median of PQR. = 10x 7, = 5x 3 and m PSR = (15x + 42). Solve for x. P Q S R 109. Given,, are the midpoints of the sides of : a) Write an equation to find the value of. b) Find the value of. c) Find. M 2x P 10x 26 N 2y d) Write an equation to find the value of. e) Find the value of. 12
13 110. Given the picture below, find : RT = I = x = R 48 U S I 6x - 12 T 111. Verify the Midsegment Theorem for DE in below. Slope DE = (2, 2) Slope = DE = (-4, -2) E(2, -2) = D(-1, -4) (2, 6) Explain your conclusion using complete sentences: 13
14 Polygons Identify if each shape is a polygon. If it is, state if it is convex or concave For questions , fill in the table. Polygon Sum of Interior ngles Sum of Exterior ngles 115. Heptagon 116. Dodecagon gon For questions , fill in the table. Regular Polygon Each Interior ngle Each Exterior ngle 118. Octagon 119. Decagon gon For questions , an interior angle measure is given. Name the regular polygon For questions , an exterior angle measure is given. Name the regular polygon pentagon has angle measures of (3x + 15), (2x + 6), (3x 24), (5x 18), and (5x + 3). Find the measure of the largest angle. 14
15 Similar Triangles Geometry P Midterm Exam Review Given WXY ~ LMN, with a scale factor of, if = 5, find. For questions , solve for the variables in each diagram is the angle bisector of D 3 6 x E 8 x D 6 y 131. is the angle bisector of x D 15 x x
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