MATH II SPRING SEMESTER FINALS REVIEW PACKET

Transcription

1 Name Date Class MATH II SPRING SEMESTER FINALS REVIEW PACKET For 1 2, use the graph. 6. State the converse of the statement. Then determine whether the converse is true. Explain. If two angles are vertical angles, then they are congruent. 1. Which segment is congruent to EF? 7. Use the graph. 2. What is the midpoint of GH? Use the following information for 3 4. In the figure, m KJL = 32. Write the vector that maps RST to R S T. Use the figure for What is the value of x? 4. What is m KJM? 5. Line segment PQ with endpoints P(4, 2) and Q( 2, 0) is rotated 90 clockwise around the origin. What are the coordinates of the midpoint of PQ? 8. How many lines of symmetry does the figure have? 9. What are the angles of rotation less than 360 for the figure? 191

2 Name Date Class Use the following information for In the figures below, ABC LNM. 15. In the figure, m 2 = What is the value of x? 11. What is the value of y? Use the following information for ABCD is a quadrilateral with BE ED and BCD DAB. 12. If EC = 20 cm and AE = 3x 4, for what value of x is ABCD a parallelogram? 13. If m DAB = (4y 12) and m ABC = 64, for what value of y is ABCD a parallelogram? 14. If ABCD is a parallelogram, BD = 3x 15, AC = x + 9, and AED = 2y + 18, for what value of x and y is the figure a square? Explain your reasoning. What is m 7? 16. The measures of two complementary angles are represented by the expressions (3x + 16) and (5x + 18). Find the value of x. 17. Write an equation for the line that passes through (1, 3) and is perpendicular to 1 y = x Write an equation for the line that passes through (3, 2) and is parallel to 2x + 3y = In the figure, the measure of 2 is 55. What is the measure of 4? 192

3 Name Date Class 20. Use the figures. 24. In the figure, PQ PS. Determine the value of x that ensures that the triangles are congruent. For 21-22, state the additional congruency statement or statements needed to prove ABC XYZ for the given theorem. Explain why PQR PSR. 25. In the figure, m BAC = 9x + 4 and m BAD = 3x ASA Theorem 22. AAS Theorem 23. Look at the figure below. What value of x indicates that AD is the angle bisector of BAC? 26. Use the figure. What is the value of x? Are triangles DEF and FGH congruent? Explain why or why not. If the triangles are congruent, write a congruence statement. 27. The sum of the measures of the interior angles of a regular polygon is 900. How many sides does the polygon have? 193

4 Name Date Class 28. Triangle RST is an isosceles triangle with m R = 120. What is m S? Explain your reasoning. 31. Quadrilateral ABCD is shown. 29. The sides of a triangle measure 5 meters and 8 meters. What are the possible side lengths for the third side? Show your work. 30. In the figure, MN is the midsegment of JKL. What is m D? 32. State whether each quadrilateral has congruent diagonals. A parallelogram Yes No B rhombus Yes No C rectangle Yes No D isosceles trapezoid Yes No E kite Yes No 33. GIJL is a trapezoid with midsegment HK. If KM = 11 cm and KL = 24 cm, what is KN? If IJ = 18 cm and GL = 42 cm, what is HK? 194

5 Name Date Class Use the following information for Triangle ABC has vertices A( 6, 2), B( 2, 2), and C(4, 8). Dilate ABC using 38. Use the figure to find the unknown distance. a factor of 1 2 about the origin. Then dilate its image using a scale factor of 5 about the origin. 34. Determine the coordinates of the final image. 35. Determine the scale factor you could use to dilate ABC about the origin that would result in the final image in one step. Use the figure for What is the distance across the river? 39. Rectangles ABCD and EFGH are similar. Rectangle ABCD has a length of 20 cm and a perimeter of 60 cm. Rectangle EFGH has a length of 32 cm. Find the area of rectangle EFGH. 40. Use the figure. 36. Which triangles are similar? Write a similarity statement. 37. What is AB? What is the length of FE? 195

6 Name Date Class Use triangle XYZ for Round to the nearest tenth. 45. In the figure, m KJL = (12x + 8) and m KML = (10x + 16). 41. What is YX? 42. What is YZ? What is the value of x? 46. In the circle, mwx = 50 and myz = 130. Use the triangle below for questions Round to the nearest tenth. What is m V? 43. If m A = 50, m B = 100, and b = 15 cm, what is a? Use the circle for In the circle, mad = 38 and mbc = If a = 12 cm, b = 18 cm, and c = 8 cm, what is m A? 47. What is m AED? _ 48. If DE = 3, EB = 16, and AE = 4, what is EC? 196

7 Name Date Class Use the circle for A right cone has a slant length of 9 centimeters and a radius of 4 centimeters. What is the surface area of the cone? Round to the nearest tenth of a square centimeter. 49. Find the exact arc length of QR. 50. Convert the central angle to radians. 57. The triangular prism has a surface area of 510 square meters. Find the missing value for x. 51. What is the area of the sector formed by RPQ to the nearest tenth? 52. Write an equation of a circle with center (3, 4) and radius 2. Use the information for A prism has 6-inch square bases and a height of 10 inches. A cylinder has a diameter of 10 inches and a height of 6 inches. 53. Which solid has the greater volume? 54. Which solid has the greater surface area? 58. A square pyramid and a cube have equal volumes. The side length of the base of each figure is 16 millimeters. How many times taller is the pyramid than the cube? 59. A cylinder has a radius of 8 inches and a height of 16 inches. The radius of a cone is half the length of the radius of the cylinder. 60. A company sells several sizes of the same design of trash cans. The trash cans consist of a cylinder and a hemisphere. The smallest size trash can has the dimensions shown. Find the volume. 55. The oblique cylinder shown below (other column) has a volume of 36π cubic inches. What is the radius of the base of the cylinder to the nearest tenth of an inch? 197