Geometry 1 st Semester Exam REVIEW Chapters 1-4, 6. Your exam will cover the following information:
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1 Geometry 1 st Semester Exam REVIEW Chapters 1-4, 6 Your exam will cover the following information: Chapter 1 Basics of Geometry Chapter 2 Logic and Reasoning Chapter 3 Parallel & Perpendicular Lines Chapter 4 Triangle Congruence Chapter 6 Polygons The exam will consist of 60 multiple choice questions. You will have a double class period to complete your exam. You will be provided with graph paper and the reference paper used for the end of course exams (by the state of Ohio). This exam is separate from the 1 st and 2 nd quarter grades. Semester grades are calculated as follows: 1 st 9- weeks: 40% of semester grade 2 nd 9- weeks: 40% of semester grade semester exam: 20% of semester grade This exam is extremely important to ensure a good grade for first semester. Please prepare yourself properly by completing all review problems attached. This review will be due on the day of your exam. Please bring it with you to the exam.
2 Chapter 1 Basics of Geometry: 1. (a) What does the symbol AB represent? (b) What does the symbol AB represent? (c) What does the symbol AB represent? 2. Classify the following angles: (a) 25 (b) 90 (c) 178 (d) 180 (e) 39 #3-5 Use the diagram below. 3. Identify three collinear points. 4. Identify two opposite rays. 5. Does point F lie on BC!!!!!? 4. Find the midpoint of a segment with endpoints: (a) (- 9, 1) and (5, - 3) (b) (12, - 8) and ( - 4, 10) 5. PT bisects RPS. m RPT is shown to be 39. What is the measure of RPS? 6. The measure of A is 76. (a) Find m B if A and B are complementary. (b) Find the m C if A and C are supplementary. 7. What is the result of the construction shown below?
3 8. Use the following diagram: (a) If m 2 = 120, then m 4 =? (b) If m 1 = 50, then m 4 =? (c) If m 3 = 133, then m 1 =? (d) If m 1 = 104, then m 2 =? 9. Give three names for the angle shown below. 10. Use the diagram below where A, B, C, and D are collinear. AB=3, AD=13, and BC=CD. Find the length of BD and CD. 11. Find the distance between points C(6, 3) and D(4, 7). 12. What is m 1 if m 2 = 115? 13. Find the area AND perimeter of the shapes below. (a) (b) (c)
4 14. (a) If m 7 = 42, then m 3 =? (b) If m 5 = 30, then m 4 =? 15. Triangle ABC has vertices at (- 3, - 1), (- 1, 2) and (6, 1). What is the perimeter of triangle ABC, rounded to the nearest tenth? 16. What quadrant is not used in problem #15? 17. Find the area of the isosceles triangles shown below. 18. In 2016, Miami FL had an estimated population of around 441,000 people. The land area is estimated to be about square miles. What was the population density of Miami in 2016? #19-23 Use the diagram shown below. 19. Name a pair of vertical angles. 20. Name a pair of corresponding angles. 21. Name a linear pair of angles. 22. Name a pair of consecutive interior angles. 23. True or false? 3 5 because they are alternate interior angles.
5 Chapter 2 Logic and Reasoning: 24. Rewrite the two conditional statements below as one biconditional statement. If an angle is acute, then its measure is less than 90. If an angle has a measure less than 90, then it is an acute angle. 25. State the property that supports the statement. (a) If AB = CD, then AB CD (b) If ADC DEF, then m ADC = m DEF (c) If RS WX, and WX YZ, then RS YZ. #26-27 Use the partial proofs shown below. Fill in the blank statements and reasons Circle ALL statements that are true about the diagram shown. A = 180 because they are a vertical angles B. 7 5 because they are vertical angles C = 180 because they are a linear pair D = 180 because they are a linear pair E. m 7 = m 5 because they are a linear pair F. m 7 = m 5 because they are vertical angles G. m 5 = m 6 because they are a linear pair H = 180 because they form a linear pair
6 Chapter 3 Parallel & Perpendicular Lines: 29. Stacey asked Julian what parallel lines are. Julian responded They are lines that never intersect and. What other part of the definition does Julian need to include in his answer to be correct? 30. Write an equation of a line with a y- intercept of 10 and is: (a) parallel to the line y =!! x + 9 (b) perpendicular to the line y =!! x Given the following equations: A. y =! x + 9! B. y =! x 5! C. y =! x + 1! D. y =! x 6! E. y =! x 2! (a) Identify which two lines are parallel. (b) Identify which two lines are perpendicular. 32. Determine if the following lines are parallel, perpendicular, or neither. (a) y = 3x 4 (b) y =! x 10! 6y + 2x = 36 8y = 2x The equation for line A is y =! x + 4.! (a) Lines A and B are parallel. Identify the correct slope of line B. (b) Lines A and C are perpendicular. Identify the correct slope of line C. 34. Find the equation of a line perpendicular to y =! x + 1 and passes through the point (- 2, 1).! 35. Find the equation of a line parallel to y =! x + 1 and passes through the point (10, 2).!
7 36. Can the lines be proven parallel? Is so, what theorem(s) would you use? (a) (b) (c) (d) (e) (f) 37. Circle all the ways that can be used to prove two lines parallel. A) alternate exterior angles theorem B) linear pair angles theorem C) alternate interior angles theorem D) corresponding angles theorem E) vertical angles theorem F) consecutive interior angles theorem 38. The lines shown are parallel. Solve to find the value of x. State which theorem you used. (a) (b)
8 Chapter 4 Triangle Congruence: 39. Classify the triangle by its angles and sides. (a) (b) (c) 40. A triangle has side lengths of 2 cm and 5 cm. Give a possible side length for the third side of the triangle. 41. In the following triangle, choose what side lengths could possible represent x, the third side of the triangle. Select ALL that apply: (a) 18 (b) 3 (c) 5.5 (d) 2 (e) Choose which postulate or theorem that can be used to prove the triangles congruent. (a) (b) (c) (d) (e) (f)
9 43. State the property used to mark the diagram. (a) ACB ECD (b) AC AC (c) A L 44. Complete the 2- column proof to prove ΔARP ΔLRN. Statements Reasons 1. PR!!!! NR!!!! 1. Given 2. PA!!!!! LN!!!! 2. Given 3. P N ARP LRN ΔARP ΔLRN In the diagram below, AC CA is an example of the property. 46. Solve for the missing angles in the triangles shown. Both triangles are isosceles. (a) If m B = 46, find m A and m C (b) Find the values for x and y. 47. Identify the shortest and longest sides of the triangle shown below.
10 48. Find all the missing angle measures. 49. Complete the following congruence statements: (a) If ABC DEF, then C. (b) If ABC DEF, then FD. (c) If ABC DEF, then BCA. 50. Isosceles EFG is shown below, where FH is an angle bisector. Complete lines 3 and 4. Chapter 6 Polygons: #51-53 (a) Name the polygon by the number of sides. (b) Classify the polygon as convex or concave Fill in the blanks. (a) A polygon with ten sides is called a. (b) A polygon with sides is called a heptagon. (c) A polygon with all equal sides is classified as. (d) A polygon with all equal sides and all equal angles is considered.
11 55. The proof shows that opposite angles of a parallelogram are congruent. Fill in the missing reason. 56. Classify the quadrilateral using the most specific name. (a) (- 1, - 3), (1, - 1), (3, - 3), (1, - 5) (b) (0, 4), (- 2, 2), (3, 2), (5, 4) (c) (5, 5), (8, 4), (5, 3), (2, 4) 57. Find the missing angles measures in the polygons. (a) Find the measure of x (b) Find the measure of x (c) Find m A and m H (d) Find m A, m B, and m D
12 58. The midsegment of the trapezoid is RT. Find the value of x. (a) (b) 59. Is there enough information to prove that the quadrilateral is a parallelogram? (a) (b) (c) (d) 60. Rhombus ABCD is shown below. Find the indicated measures. 61. DEFG is a parallelogram. Find the indicated measures. m D = EH = y = x = 62. Three vertices are provided for parallelogram PQRS. What is the coordinate of point P to make the indicated shape? (a) Q(0, 5), R(- 2, 2), S(0, - 1) Rhombus (b) Q(- 1, 2), R(- 3, 0), S(1, - 4) Rectangle (c) Q(- 3, 0), R(- 2, 4), S(4, 4) Parallelogram
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