Course 2 Unit 4 Practice
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1 Course 2 Unit 4 Practice Lesson Model with mathematics. Two angles are supplementary. One measures (3x)8 and the other measures 518. a. Draw a pair of adjacent, supplementary angles and label them using the given information. 3. What is the measure of /ABC? A. 278 C 638 A B D B. 638 C D b. Write an equation to show the relationship between the two angles and solve for the value of x. 4. Use appropriate tools strategically. /R and /S are supplementary. m/r and m/s 5 (4x 1 3)8. Find the value of x. c. Find the measure of both angles. Show your work. 2. What is the measure of /ABC? A 5. /ZTS and /NRQ are supplementary. m/zts 5 (6x 2 10) and m/nrq 5 (3x 1 1). Find the measure of each angle. C B 388 D A. 388 B. 528 C. 648 D College Board. All rights reserved. 1 SpringBoard Course 2, Unit 4 Practice
2 Lesson Use the diagram. 9. Find the measure of x in the diagram x a. Find the measure of /1. b. Find the measure of /2. A. 29 degrees B. 45 degrees C. 51 degrees D. 65 degrees c. Find the measure of / Persevere in solving problems. Use the diagram to find the measures of each of the angles in the triangles. 7. Reason quantitatively. Find the measure of each of the angles in the triangle shown A B C 398 D E (x 1 6) x 1 15 Lesson Determine whether it is possible to draw a triangle with the given side lengths. Justify your answers. a. 8 feet, 6 feet, and 3 feet 8. /A and /B are vertical angles. m/b 5 (3x 1 4)8 and m/a 5 (x 1 48)8. Find the measure of angle A. A. 22 degrees B. 66 degrees C. 70 degrees D. 72 degrees b. 4 meters, 5 meters, and 7 meters c. 6 inches, 8 inches, and 16 inches d. 7 yards, 14 yards, and 7 yards 2
3 12. Make use of structure. Two sides of a triangle measure 4 inches and 7 inches. What is one possible length for the third side of the triangle? Explain. Lesson Construct viable arguments. Determine whether the given conditions determine a unique triangle or more than one triangle. Justify your answers. a. Two angles of a triangle measure 428 and 778. The side between the angles is 4 feet long. 13. Model with mathematics. Draw a triangle with side lengths that are 7 centimeters, 9 centimeters, and 11 centimeters. b. Two angles of a triangle each measure 568. The side opposite one of the 568 angles is 3 meters long. 14. Which of the following cannot be the side lengths of a triangle? A. 5 inches, 5 inches, 5 inches B. 4 inches, 4 inches, 3 inches C. 16 centimeters, 17 centimeters, 18 centimeters D. 4 centimeters, 12 centimeters, 25 centimeters c. The angles of a triangle measure 508, 608, and Which of the following could be the length of the third side of a triangle with side lengths of 3 feet and 12 feet? A. 15 feet B. 13 feet C. 20 feet D. 9 feet d. The sides of a triangle are 10 inches, 24 inches, and 26 inches long. 3
4 17. Which condition results in more than one triangle? A. The angles of a triangle measure 268, 728 and 828. B. Two angles of a triangle measure 858 and 688. The side between the angles is 3 meters long. C. Two sides that form a right angle of a triangle are 6 inches and 8 inches long. D. Two angles of a triangle each measure 638. The side opposite one of the 638 angles is 32 inches long. Lesson nabc, ndef, m/a 5 28 and m/e What is the measure of angle C? A B C. 508 D Construct viable arguments. Rectangle ABCD is 8 feet by 10 feet. Rectangle EFGH is 16 feet by 20 feet. 18. Which condition results in more than one triangle? A. Two angles of a triangle each measure 658. The side opposite one of the 658 angles is 24 inches long. B. Two angles of a triangle measure 828 and 628. The side between the angles is 5 meters long. C. Two sides that form a right angle of a triangle are 10 inches and 12 inches long. D. Two sides of a triangle are 4 meters and 7 meters long. One of the non-included angles measures Reason abstractly. When a triangle is formed by three given sides, is the triangle a unique triangle, or can more than one triangle be formed using those same three sides? Explain. A 8 ft 16 ft D 10 ft B C a. Name the corresponding angles. b. Name the corresponding sides. 20 ft c. Write the ratios of the corresponding widths and lengths of the rectangles. d. Are the corresponding sides in proportion? Explain. E H F G 20. Is it possible to draw a unique triangle with two sides that are each 15 centimeters long and an included angle that measures 428? Explain. e. Is rectangle ABCD similar to rectangle EFGH? Explain. 23. Model with mathematics. Sketch two similar figures. Explain why they are similar. 4
5 24. Are the ratios of the corresponding sides of the right triangle shown equal? Explain A rectangular room is 48 feet wide and 72 feet long. On a blueprint, the room is 26 inches wide. How long is the room on a blueprint? A. 24 inches B. 36 inches C. 39 inches D. 42 inches Rectangle J is 8 feet wide and 12 feet long. Rectangle K is 9 feet wide and 15 feet long. Rectangle L is 13.5 feet wide and 22.5 feet long. Which statement is true? A. Rectangle J, Rectangle K B. Rectangle K, Rectangle L C. Rectangle J, Rectangle L D. All of the triangles are similar Lesson nabc, ndef. Find the measures of the missing sides. 28. Model with mathematics. A flagpole casts a shadow 9 feet long. At the same time, a small tree 4 feet tall casts a shadow 3 feet long. a. Draw and label a picture to model the situation. b. Write and solve a proportion to determine the height of the flagpole. B 27? E 29. A lighthouse casts a 72-foot-long shadow at the same time a nearby building that is 12 feet tall casts an 18-foot-long shadow. What is the height of the lighthouse? A. 36 feet? 14 B. 48 feet C. 52 feet A 12 C D 8 F D. 108 feet 5
6 30. Make sense of problems. Nicholas is 5 feet 2 inches tall. On a sunny day he casts a shadow that is 3 feet long. At the same time, a nearby pole casts a shadow 15 feet 6 inches long. How tall is the pole? 34. Make sense of problems. The diameter of a bicycle tire is 22 inches. About how many revolutions does the wheel make during a ride of 600 feet? Use 3.14 for p. Explain your answer. Lesson What is the circumference of a circle with a radius of 5 feet? A ft B ft C ft D. 157 ft 35. Make use of structure. A circle has a circumference of cm. What is the diameter of the circle to the nearest centimeter? What is the radius to the nearest centimeter? 32. A port hole on a freight ship has a radius of 18 inches. What is the length of the insulating strip that encircles the window? 33. What is the circumference of the circle shown? Lesson What is the area of a circle with a radius of 8 feet? A ft 2 B ft 2 C ft 2 D ft What is the area of the circle shown? 20 mm A mm B mm C mm D. 314 mm A cm 2 B cm 2 C cm 2 D cm 2 14 cm 6
7 38. The circumference of a circle is cm. What is the area of the circle? cm 20 cm 8 cm 11 cm 39. Persevere in solving problems. There is a brick patio around a fire pit. Use 3.14 for p. a. Draw a line segment on the diagram to divide the figure into a rectangle and a triangle. b. Find the total area of the composite figure. Show your work. Label your answer with the appropriate unit of measure. 2 ft 5 ft c. Find the perimeter of the composite figure. Show your work. Label your answer with the appropriate unit of measure. a. What is the area of the fire pit? 42. If the total base length of the triangle shown is 12 feet, what is the area of just the triangle to the right of the dashed vertical line? b. What is the area of the brick patio? 8 ft Lesson Reason quantitatively. A 16-inch pizza costs $ The pizza is cut into eight equal slices. How many square inches are in each slice? Show your work. A. 12 ft 2 B. 24 ft 2 C. 36 ft 2 D. 72 ft 2 3 ft 43. Make sense of problems. A 5-inch wide by 7-inch long photo is placed on a solid mat that forms a frame around it. The mat is 12 inches wide. The mat and the photo are similar rectangles. What is the area of the mat? 7
8 44. What is the perimeter of the composite figure? cm 3 cm 8 ft 15 ft a. What is the diameter of the semicircle? 22 cm 8 cm 6 cm b. Find the total area of the figure. Use 3.14 for p. Show your work. 15 cm A. 72 cm B. 83 cm C. 84 cm D. 96 cm c. Find the distance around the figure. Show your work. 45. Reason quantitatively. A kite is formed by connecting the bases of two triangular frames. The height of the top frame is 12 inches. The height of the lower section is 18 inches. The bases of the frames are 14 inches long. What is the least amount of material needed to make three kites? 48. What is the area of the shaded region? 16 cm Lesson What is the area of the shaded region? 20 cm 8 cm 14 cm 5 cm A. 40 cm 2 B. 240 cm 2 C. 280 cm 2 D. 320 cm 2 A cm 2 B cm 2 C cm 2 D cm Make sense of problems. A circular pizza has a diameter of 12 inches. A pizza in the center of the pan has a radius of 4 inches. How much of the pan is not covered by the pizza? Use 3.14 for p. 8
9 50. Reason quantitatively. A banner is being made for the opening of an ice-cream parlor. On the banner is an ice-cream cone a triangular height of 10 feet and the base of the semicircle is 6 feet. What is the total area of the ice-cream cone? Use 3.14 for p. Show your work. 53. How many sides does a pentagonal pyramid have? A. 4 B. 5 C. 6 D. 7 Lesson Model with mathematics. 54. In a right rectangular pyramid, what cross section is not possible? a. What is the name of the solid formed by this net? b. What are the horizontal and vertical cross sections of the solid? A. rectangle B. square C. triangle D. trapezoid 55. Reason abstractly. Is it possible to have a circular cross section of a triangular prism? Explain. 52. What is the horizontal cross section of the figure shown? 9
10 Lesson Model with mathematics. 4 km 4 km 4 km 58. What is the surface area of the prism? 6 in. 8 in. 4 km 12 in. 12 in. 7 km 10 in. 4 km 4 km a. Find the area of each lateral face. Show your work. A. 318 in. 2 B. 336 in. 2 C. 376 in. 2 D. 390 in. 2 b. Find the lateral area of the solid. Show the work. c. Determine the perimeter of the base. 59. What is the surface area of the prism? 5 feet 57. Model with mathematics. 3 feet 5 ft 4 feet 9 feet A. 93 ft 2 9 ft 3 ft a. Find the lateral area of the prism. B. 114 ft 2 C. 120 ft 2 D. 132 ft 2 b. Find the surface area of the prism. 10
11 60. Attend to precision. Which two surfaces must you add to the lateral area when finding the surface area of a rectangular prism? 63. A square pyramid has a base length of 825 feet. The slant height of this large pyramid is 596 feet. What is the lateral area of the pyramid? A. 245,850 ft 2 B. 491,700 ft 2 Lesson Model with mathematics. What is the surface area of the pyramid? 9 ft C. 983,400 ft 2 D. 1,664,025 ft Make use of structure. A holiday decoration is constructed from two square pyramids that are joined together at their bases. The edge of each square base is 4.5 inches. The slant height of the triangular faces is 7 inches. What is the surface area of the decoration? 5.5 ft 5.5 ft A. 99 ft 2 B ft 2 C. 154 ft 2 D ft Persevere in solving problems. The base of a triangular pyramid has sides that are 6 cm long and a height of 10.3 cm. The slant height of the pyramid is 10.3 cm. a. Find the lateral area of the pyramid. Show your work. 65. A square pyramid has a slant height of 7 feet. The perimeter of the base is 42 feet. Find the surface area of the pyramid. b. Find the surface area of the pyramid. Show your work. 11
12 Lesson Model with mathematics. What is the volume of the prism? 69. How many cubes with side length of 4 inches will fit into the rectangular prism? Explain. 8 in. 8 ft 36 in. 12 in. 9 ft 3 ft 67. A cube has a face area of 64 square centimeters. What is the volume of the cube? A. 16 cm 3 B. 24 cm 3 C. 384 cm 3 D. 512 cm Make sense of problems. Byron is considering buying two different fish tanks. The first one is 2 feet long, 15 inches wide and 26 inches deep. The second one is 2 feet long, 18 inches wide and 28 inches deep. How much more water is needed to fill the second one than the first? 68. What is the volume of the triangular prism? 8 in. 12 in. 10 in. A. 688 in. 3 B. 768 in. 3 C. 960 in. 3 D in. 3 12
13 Lesson Model with mathematics. 16 cm 73. Reason abstractly. A square pyramid with the base length of 16 inches is 24 inches tall. The top part of the pyramid is cut off to form a small pyramid with base length of 8 inches and height of 12 inches. How many cubic inches greater was the volume of the larger pyramid than that of the new smaller pyramid? 20.5 cm 74. What is the volume of the figure? 12 cm 8 mm 20.5 cm a. Find the volume of the rectangular prism. 14 mm b. Find the volume of the rectangular pyramid. c. Find the total volume of the complex solid. A mm3 B. 112 mm 3 C mm3 14 mm 72. A square pyramid is 21 inches tall and has a volume of 1372 in. 3 How long is each side of the base of the pyramid? A. 14 inches B inches C. 21 inches D inches D. 896 mm Two square pyramids are joined at their bases. Each base is 28 cm long. The distance between the vertices of the combined pyramids is 21 cm. What is the volume of the solid formed? 13
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