Hon Geometry Midterm Review

Transcription

1 Class: Date: Hon Geometry Midterm Review Multiple Choice Identify the choice that best completes the statement or answers the question. Refer to Figure 1. Figure 1 1. Name the plane containing lines m and p. a. n c. H b. GFC d. JDB 2. Name three points that are collinear. a. B, G, F c. J, G, F b. C, D, H d. J, D, G 1

2 Refer to Figure 2. Figure 2 3. Name four points that are coplanar. a. G, D, L, B c. L, A, C, G b. C, K, A, G d. K, B, D, L Use the figure to find the angles. 4. Name an angle supplementary to!mqi. a.!iqg c.!mqk b.!gql d.!iqh Determine whether the conjecture is true or false. Give a counterexample for any false conjecture. 5. Given: points R, S, and T Conjecture: R, S, and T are coplanar. a. False; the points do not have to be in a straight line. b. True c. False; the points to not have to form right angles. d. False; one point may not be between the other two. 2

3 6. Given: segments RT and ST; twice the measure of ST is equal to the measure of RT. Conjecture: S is the midpoint of segment RT. a. True b. False; point S may not be on RT. c. False; lines do not have midpoints. d. False; ST could be the segment bisector of RT. Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample. 7. An equilateral triangle has three congruent sides. a. A non-equilateral triangle has three congruent sides. False; an isosceles triangle has two congruent sides. b. A figure that has three non-congruent sides is not an equilateral triangle. True c. A non-equilateral triangle does not have three congruent sides. True d. A figure with three congruent sides is an equilateral triangle. True Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample. 8. A converse statement is formed by exchanging the hypothesis and conclusion of the conditional. a. A non-converse statement is not formed by exchanging the hypothesis and conclusion of the conditional. True b. A statement not formed by exchanging the hypothesis and conclusion of the conditional is a converse statement. False; an inverse statement is not formed by exchanging the hypothesis and conclusion of the conditional. c. A non-converse statement is formed by exchanging the hypothesis and conclusion of the conditional. False; an inverse statement is formed by negating both the hypothesis and conclusion of the conditional. d. A statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement. True 3

4 In the figure below, points A, B, C, and F lie on plane P. State the postulate that can be used to show each statement is true. 9. A and B are collinear. a. If two points lie in a plane then the entire line containing those points lies in that plane. b. Through any two points there is exactly one line. c. If two lines intersect then their intersection is exactly one point. d. A line contains at least two points. Refer to the figure below. 10. Name all planes intersecting plane CDI. a. ABC, CBG, ADI, FGH c. BAD, GFI, CBG, GFA b. CBA, DAF, HGF d. DAB, CBG, FAD 11. Name all segments skew to HI. a. BC, AD, AF, BG c. AD, AB, BC, CD b. FI, GH, DI, CH d. BA, BG, AF, FG 4

5 Identify the sets of lines to which the given line is a transversal. 12. line a a. lines c and b f and d c and f c and d b and d b. lines a and b a and c a and d a and f c. lines f and d c and f c and d b and d d. lines c and b f and d Determine whether "PQR # "STU given the coordinates of the vertices. Explain. 13. P Ê Ë Á $3, 2 ˆ, Q Ê Ë Á$2, $ 3 ˆ, R Ê Ë Á$1, 4 ˆ, S Ê Ë Á2, 4 ˆ, T Ê Ë Á3, $ 1 ˆ, U Ê ËÁ 4, 6 ˆ a. Yes; Both triangles have three acute angles. b. No; Each side of triangle PQR is not the same length as the corresponding side of triangle STU. c. No; Two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU. d. Yes; Each side of triangle PQR is the same length as the corresponding side of triangle STU. 5

6 Identify the type of congruence transformation. 14. a. reflection c. rotation b. translation d. not a congruence transformation Position and label the triangle on the coordinate plane. 15. right isosceles "ABC with congruent sides AB and AC a units long a. c. b. d. 6

7 Refer to parallelogram ABCD to answer to following questions. 16. Are the diagonals congruent? Justify your answer. a. Yes; Both diagonals have a length of b. Yes; Both diagonals have a length of 6 2. c. Yes; Both diagonals have a length of 3 2. d. No; The lengths of the diagonals are not the same. Short Answer Refer to Figure 1. Figure Name the intersection of lines m and n. 7

8 Refer to Figure 2. Figure How many planes are shown in the figure? 19. Name the intersection of plane KCG and a plane that contains points L and D. Find the measurement of the segment. 20. QT = 0.4 in., QV = 1.9 in. TV =? 21. Find the value of the variable and LN if M is between L and N. LM = 8a, MN = 7a, LM = 56 Use the number line to find the measure. 22. PH 8

9 Use the Distance Formula to find the distance between each pair of points. 23. Find the coordinates of the midpoint of a segment having the given endpoints. 24. Q Ê Ë Á $0.4, 2.5 ˆ, R Ê ËÁ 3.5, 1.5 ˆ In the figure, KJ && % and KL && % are opposite rays.!1 #!2 and KM &&% bisects!nkl. 25. If m!jkp = 3r + 12 and m!2 = 4r $ 2, what is m!jkn? 26. If m!lkn = 6w $ 10 and m!jkp = 2w + 5, what is w? 27. The measures of two complementary angles are 12q $ 9 and 8q Find the measures of the angles. 28. The measure of an angle s supplement is 24 less than twice the measure of the angle. Find the measure of the angle and its supplement. 9

10 Name each polygon by its number of sides. 29. Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular. 30. Find the length of each side of the polygon for the given perimeter. 31. P = 48 cm 10

11 Find the circumference of the figure. 32. Find the area of the figure

12 35. Name the bases of the solid. 36. Name the bases of the prism. Name the edges of the solid Find the surface area of the solid. 12

13 39. Make a conjecture about the next item in the sequence , 8, $ 32, $ 30, 120 Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value. p: An isosceles triangle has two congruent sides. q: A right angle measures 90 r: Four points are always coplanar. s: A decagon has 12 sides. 41. q ' p 42. s ( p Determine whether statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of Syllogism. If it does, state which law was used. If it does not, write invalid. 43. (1) You are in ninth grade. (2) People who are in ninth grade floss their teeth regularly. (3) You floss your teeth regularly. 44. In the figure, m!nml = 120, )&& PQ % Ä )& TU % )& % )&& % and KL Ä NM. Find the measure of angle PRK. 13

14 45. In the figure, AB Ä CD. Find x and y. Determine whether )&& WX % and )& YZ % are parallel, perpendicular, or neither. 46. W Ê Ë Á $2, $ 1 ˆ, X Ê Ë Á4, 1 ˆ, Y Ê Ë Á1, $ 4 ˆ, Z Ê ËÁ 5, $ 4 ˆ Write an equation in slope-intercept form of the line having the given slope and y-intercept. 47. m: $ 4 5, Ê ËÁ 0, $ 3 ˆ Write an equation in point-slope form of the line having the given slope that contains the given point. 48. m = 5, Ê30, 12 6 ËÁ ˆ 49. m = 3, Ê36, 24 4 ËÁ ˆ Find the distance between the pair of parallel lines. 50. y = 4x + 4 y = 4x $ 4 Find the measures of the sides of "ABC and classify the triangle by its sides. 51. AÊ Ë Á 3, $ 3 ˆ, B Ê Ë Á1, 4 ˆ, C Ê ËÁ $1, $ 1 ˆ 14

15 Find each measure. 52. m!1, m!2, m!3 53. m!1, m!2, m!3 Refer to the figure. "ARM, "MAX, and "XFM are all isosceles triangles. 54. What is m!amx? 55. What is m!max? 56. What is m!rax? 15

16 57. Triangle FJH is an equilateral triangle. Find x and y. 58. Triangle RSU is an equilateral triangle. RT bisects US. Find x and y. Determine the relationship between the measures of the given angles. 59.!JCQ,!RCQ Determine the relationship between the lengths of the given sides. 60. HB, BL 61. An isosceles triangle has a base 9.6 units long. If the congruent side lengths have measures to the first decimal place, what is the shortest possible length of the sides? 16

17 62. Which segment is the shortest possible distance from point D to plane P? 63. Find the measure of each interior angle for a regular pentagon. Round to the nearest tenth if necessary. 64. Find the measure of an interior angle of a regular polygon with 14 sides. Round to the nearest tenth if necessary. 65. Find the measure of each exterior angle for a regular nonagon. Round to the nearest tenth if necessary. Complete the statement about parallelogram ABCD. 66. AD # Refer to parallelogram ABCD to answer to following questions. 67. What is the length of segment DK? 68. Do the diagonals bisect each other? Justify your answer. 17

18 Determine whether the quadrilateral is a parallelogram. Justify your answer. 69. Quadrilateral ABCD is a rectangle. 70. If!ADB = 2y + 40 and!cdb = $3y + 51, find!cbd. 71. In rhombus TUVW, if m!tuw = 34, find m!uvt. Given each set of vertices, determine whether parallelogram ABCD is a rhombus, a rectangle, or a square. List all that apply. 72. A(5, 10), B(4, 10), C(4, 9), D(5, 9) 73. A($2, 6), B($2, $ 1), C($9, $ 1), D($9, 6) 18

19 74. For trapezoid JKLM, A and B are midpoints of the legs. Find ML. 75. Keith needs to buy motor oil to fill an empty cylindrical barrel at his oil service center. The barrel is feet deep and has a diameter of feet. What is the volume of oil needed? Round to the nearest tenth. Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample. 76. Two segments having the same measure are congruent. 77. Determine the converse of the conditional statement, If a triangle is acute, then it has three acute angles. State whether the converse is true or false. If the converse is false, find a counterexample. The picture below shows the drawing of a boat. Find each measure. 78. m!2 79. The face of Jesse s wristwatch is a regular hexagon. Find the measure of an interior angle and an exterior angle of the face. 80. Richard wants to buy a LCD flat panel monitor measuring 14 inches by 16 inches. What is the measure of the diagonal of the monitor? 19

20 Hon Geometry Midterm Review Answer Section MULTIPLE CHOICE 1. B 2. A 3. B 4. A 5. B 6. B 7. C 8. D 9. B 10. A 11. A 12. A 13. D 14. B 15. B 16. D SHORT ANSWER 17. D line CG in. 21. a = 7, LN = Ê ËÁ 1.55, 2 ˆ , , decagon 30. decagon, concave, irregular cm * cm in * m ña and ñb 1

21 36. "UWY and "VXZ 37. AB, AD, AC, CD, DB, and BC units units A right angle measures 90 and an isosceles triangle has two congruent sides; true. 42. A decagon has 12 sides or an isosceles triangle has two congruent sides; true. 43. yes; Law of Detachment x = 51, y = neither 47. y = $ 4 5 x $ y $ 12 = 5 (x $ 30) y $ 24 = 3 (x $ 36) d = scalene 52. m!1 = 77, m!2 = 36, m!3 = m!1 = 74, m!2 = 129, m!3 = x = 7, y = x = 1 2, y = !JCQ =!RCQ 60. cannot be determined DQ BC; Opposite sides of parallelograms are congruent Yes; AK # CK and DK # BK 69. No; Opposite angles are not congruent square; rectangle; rhombus 73. square; rectangle; rhombus

22 ft 3 The volume of a cylinder is given by V = *r 2 h. 76. Sample: Noncongruent segments are not two segments having the same measure. True. 77. Sample answer: If a triangle has three acute angles, then it is an acute triangle; true The converse of a conditional statement Ê ËÁ p % q ˆ exchanges the hypothesis and conclusion of the conditional. It is also known as q % p. The sum of the measures of the angles of a triangle is , 60 To find the measure of each interior angle of a regular polygon, use the formula 180(n $ 2). n To find the measure of each exterior angle of a regular polygon, use the formula 360 n. 80. about 21 in. Use the Pythagorean Theorem to find the length of the diagonal. 3