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Math 6 Geometry Study guide Multiple Choice Identify the choice that best completes the statement or answers the question. Find the missing measure in each triangle. Then 3. classify the triangle as acute, right, or obtuse. 1. 60° 38° 60° a. b. c. d. x° a. b. c. d. 62; right 52; right 52; acute 42; obtuse x° 60; acute 90; right 30; acute 60; obtuse 4. x° 2. 56° 60° 63° a. b. c. d. 61; right 51; acute 61; acute 65; obtuse x° a. b. c. d. 60; obtuse 90; right 30; acute 30; right c. obtuse, scalene d. acute, equilateral 5. 8. 46° 42° 9.5 9.5 x° a. b. c. d. 82; acute 90; right 78; acute 92; obtuse 70° 6.6 a. b. c. d. Classify each triangle by its angles and by its sides. 6. 4 acute, scalene right, isosceles acute, isosceles acute, equilateral Find the best name to classify each quadrilateral. 9. 3 a. b. c. d. obtuse, scalene right, scalene right, isosceles right, equilateral 7. a. b. c. d. 42° 50° 88° a. acute, scalene b. right, scalene 70° square rectangle quadrilateral parallelogram d. parallelogram 10. 13. a. b. c. d. quadrilateral rectangle trapezoid parallelogram a. b. c. d. quadrilateral rectangle square parallelogram 11. Determine whether each statement is sometimes, always, or never true. a. b. c. d. rhombus quadrilateral trapezoid parallelogram 12. 14. A trapezoid is a quadrilateral. a. sometimes b. always c. never 15. A quadrilateral is a rhombus. a. sometimes b. always c. never 16. A rectangle is a parallelogram. a. sometimes b. always c. never 17. A rectangle is a trapezoid. a. sometimes b. always c. never 18. A parallelogram is an isosceles triangle. a. sometimes b. always c. never Find the volume of each rectangular prism. Round to the nearest tenth if necessary. a. rhombus b. rectangle c. quadrilateral 19. 21. 3 mm 16.5 mm 9 mm 13.6 mm a. b. c. d. 3 mm 7.8 mm a. b. c. d. 456 mm2 190.2 mm2 380.4 mm2 102.4 mm2 22. 386.1 mm3 193.1 mm3 27.3 mm3 1,003.9 mm3 20. 12.5 yd 3.2 mm 5 yd 8 mm 4 yd 10 mm a. b. c. d. a. b. c. d. 3 21.2 mm 320 mm3 128 mm3 256 mm3 Find the surface area of each rectangular prism. Round to the nearest tenth if necessary. Short Answer Tell whether each pair of figures is congruent, similar, or neither. 23. 2 86 yd 265 yd2 318 yd2 132.5 yd2 24. 26. 4 cm 6 cm 27. 25. Find the area of each parallelogram. Round to the nearest tenth if necessary. 28. 24.7 yd 6.3 yd Find the area of each triangle. Round to the nearest tenth if necessary. 29. 20 ft 8 ft 30. 31. 6.3 m 10.4 m 32. 33. 6 mi 3 mi 34. Find the volume of each solid. Round to the nearest tenth if necessary. 39. 9.3 cm 11.5 cm 14.7 mm 35. height: 80 mm base: 14 mm 36. height: in. base: 10 in. 2.8 mm 6.7 mm Find the area to the nearest tenth. Use 3.14 for . Find the surface area of each solid. Round to the nearest tenth if necessary. 37. 40. 8 km 15 mm 5 mm 7 mm 38. 6.7 cm Essay 41. Tanika built a rectangular prism using 1-inch cubes. The prism is 6 cubes long, 3 cubes deep, and 3 cubes high. a. What is the surface area of the rectangular prism? b. What is the volume of the rectangular prism? c. Draw Tanika’s rectangular prism. Math 6 Geometry Study guide Answer Section MULTIPLE CHOICE 1. ANS: B The triangle is a right triangle. The sum of its angles is 180°. x + 90 + 38 = 180 x = 52 Feedback A B C D What is the sum of the triangle's interior angles? Correct! Are all three angles less than 90 degrees? Does the triangle contain an angle greater than 90 degrees? PTS: 1 DIF: Basic OBJ: 10-4.1 Identify triangles. TOP: Identify triangles. KEY: Triangles | Identifying triangles 2. ANS: C The triangle is an acute triangle. The sum of its angles is 180°. x + 63 + 56 = 180 x = 61 Feedback A B C D Does the triangle contain a right angle? Double check your work and try again. Correct! Does the triangle contain an angle greater than 90 degrees? PTS: 1 DIF: Average OBJ: 10-4.1 Identify triangles. TOP: Identify triangles. KEY: Triangles | Identifying triangles 3. ANS: A The triangle is an acute triangle. The sum of its angles is 180°. x + 60 + 60 = 180 x = 60 Feedback A B C D Correct! Does the triangle contain a right angle? Double check your work and try again. What is the sum of the interior angles of a triangle? Does the triangle contain an angle greater than 90 degrees? PTS: 1 DIF: Average OBJ: 10-4.1 Identify triangles. TOP: Identify triangles. KEY: Triangles | Identifying triangles 4. ANS: D The triangle is a right triangle. The sum of its angles is 180°. x + 90 + 60 = 180 x = 30 Feedback A B C D Are there any angles greater than 90 degrees? Double check your work and try again. What is the sum of the interior angles of a triangle? Are all the angles less than 90 degrees? Correct! PTS: 1 DIF: Average OBJ: 10-4.1 Identify triangles. TOP: Identify triangles. KEY: Triangles | Identifying triangles 5. ANS: D The triangle is an obtuse triangle. The sum of its angles is 180°. x + 46 + 42 = 180 x = 92 Feedback A B C D Double check your work and try again. What is the sum of the interior angles of a triangle? Be careful when solving for x. Try again. Are all the angles less than 90 degrees? Double check your work and try again. Correct! PTS: 1 DIF: Average OBJ: 10-4.1 Identify triangles. TOP: Identify triangles. KEY: Triangles | Identifying triangles 6. ANS: B The triangle has three unequal sides and a right angle. It is a right, scalene triangle. Feedback A B C D Does the triangle have an angle greater than 90 degrees? Correct! Does the triangle have two sides with the same length? What kinds of sides does an equilateral triangle have? PTS: 1 DIF: Basic OBJ: 10-4.2 Classify triangles. TOP: Classify triangles. KEY: Triangles | Classifying triangles 7. ANS: A The triangle has three unequal sides and three angles less than 90°. It is an acute, scalene triangle. Feedback A B C D Correct! Does the triangle contain a right angle? Does the triangle have an angle greater than 90 degrees? What kinds of sides does an equilateral triangle have? PTS: 1 DIF: Average OBJ: 10-4.2 Classify triangles. TOP: Classify triangles. KEY: Triangles | Classifying triangles 8. ANS: C The triangle has two equal sides and three angles less than 90°. It is an acute, isosceles triangle. Feedback A B C D Do any of the sides have the same length? Does the triangle contain a right angle? Correct! What kinds of sides does an equilateral triangle have? PTS: 1 DIF: Average OBJ: 10-4.2 Classify triangles. TOP: Classify triangles. KEY: Triangles | Classifying triangles 9. ANS: A The figure has four right angles and four congruent sides. It is a square. Feedback A B C D Correct! What is the name of a rectangle with four congruent sides? What is a more specific name for the quadrilateral? What is the name of a parallelogram with four congruent sides and four right angles? PTS: 1 DIF: Basic OBJ: 10-5.1 Identify quadrilaterals. STA: 7.9 | 7.11 TOP: Identify quadrilaterals. KEY: Quadrilaterals | Identifying quadrilaterals 10. ANS: C The figure has one pair of opposite sides parallel. It is a trapezoid. Feedback A B C D What is a more specific name for the quadrilateral? A rectangle has four right angles. Correct! A parallelogram has two pairs of opposite sides parallel. What is the name of a quadrilateral with exactly one pair of opposite sides parallel? PTS: 1 DIF: Average OBJ: 10-5.1 Identify quadrilaterals. STA: 7.9 | 7.11 TOP: Identify quadrilaterals. KEY: Quadrilaterals | Identifying quadrilaterals 11. ANS: B The figure is simply a quadrilateral. Feedback A B C D A rhombus is a parallelogram with four congruent sides. Correct! Does the figure have a pair of opposite sides that are parallel? Are the pairs of opposite sides parallel to each other? PTS: 1 DIF: Average OBJ: 10-5.1 Identify quadrilaterals. STA: 7.9 | 7.11 TOP: Identify quadrilaterals. KEY: Quadrilaterals | Identifying quadrilaterals 12. ANS: D The figure has two pairs of opposite sides that are congruent. It is a parallelogram. Feedback A B Are all four sides of the figure congruent? A rectangle is a parallelogram with four right angles. C D What is a more specific name for the quadrilateral? Correct! PTS: 1 DIF: Average OBJ: 10-5.1 Identify quadrilaterals. STA: 7.9 | 7.11 TOP: Identify quadrilaterals. KEY: Quadrilaterals | Identifying quadrilaterals 13. ANS: B The figure is a parallelogram with four right angles. It is a rectangle. Feedback A B C D What is a more specific name for the quadrilateral? Correct! Are all four sides of the figure congruent? What is the name for a parallelogram with four right angles? PTS: 1 DIF: Basic OBJ: 10-5.1 Identify quadrilaterals. STA: 7.9 | 7.11 TOP: Identify quadrilaterals. KEY: Quadrilaterals | Identifying quadrilaterals 14. ANS: B Every trapezoid has four sides, so a trapezoid is always a quadrilateral. Feedback A B C Try to draw a trapezoid that is not a quadrilateral. Correct! How many sides does a trapezoid have? PTS: 1 DIF: Basic OBJ: 10-5.2 Classify quadrilaterals. STA: 7.9 | 7.11 TOP: Classify quadrilaterals. KEY: Quadrilaterals | Classifying quadrilaterals 15. ANS: A A quadrilateral is sometimes a rhombus, but it can also be a trapezoid, or a parallelogram, etc. Feedback A B C Correct! Is it possible to draw a quadrilateral that is not a rhombus? How many sides does a rhombus have? PTS: 1 DIF: Average OBJ: 10-5.2 Classify quadrilaterals. STA: 7.9 | 7.11 TOP: Classify quadrilaterals. KEY: Quadrilaterals | Classifying quadrilaterals 16. ANS: B A rectangle is a parallelogram with four right angles, so it is always a parallelogram. Feedback A B C Is it possible to draw a rectangle that is not a parallelogram? Correct! Are the opposite sides of a rectangle parallel? PTS: 1 DIF: Average OBJ: 10-5.2 Classify quadrilaterals. STA: 7.9 | 7.11 TOP: Classify quadrilaterals. KEY: Quadrilaterals | Classifying quadrilaterals 17. ANS: C A rectangle is a parallelogram and a trapezoid has exactly one pair of opposite sides parallel, so a rectangle can never be a trapezoid. Feedback A B C Is it possible to draw a rectangle with exactly one pair of opposite sides that are parallel? How many pairs of opposite parallel sides does a rectangle have? Correct! PTS: 1 DIF: Average OBJ: 10-5.2 Classify quadrilaterals. STA: 7.9 | 7.11 TOP: Classify quadrilaterals. KEY: Quadrilaterals | Classifying quadrilaterals 18. ANS: C A parallelogram has four sides and can never be a triangle. Feedback A B C How many sides does a parallelogram have? Do parallelograms and isosceles triangles have the same number of sides? Correct! PTS: 1 DIF: Basic OBJ: 10-5.2 Classify quadrilaterals. STA: 7.9 | 7.11 TOP: Classify quadrilaterals. KEY: Quadrilaterals | Classifying quadrilaterals 19. ANS: A Sample: 13 cm 5 cm 9 cm Use the formula V = Bh. V = (9)(5)(13) V = 585 cm3 Feedback A B C D Correct! The volume of a prism is the product of the area of its base and its height. What operation is used to calculate volume? What is the area of the base of the prism? PTS: 1 DIF: Average OBJ: 12-2.1 Find the volumes of rectangular prisms. STA: 7.8 TOP: Find the volumes of rectangular prisms. KEY: Volume | Prisms 20. ANS: D Sample: 6 mm 5.9 mm 8.1 mm Use the formula V = Bh. V = (8.1)(5.9)(6) V = 286.74 mm3 Feedback A B C D What operation is used to calculate volume? What is the area of the base of the prism? The volume of a prism is the product of the area of its base and its height. Correct! PTS: 1 DIF: Average OBJ: 12-2.1 Find the volumes of rectangular prisms. STA: 7.8 TOP: Find the volumes of rectangular prisms. KEY: Volume | Prisms 21. ANS: C Sample: 6 cm 8.4 cm 10 cm Find the area of each of the six faces. Add these together to find the total surface area. SA = 2(10)(8.4) + 2(8.4)(6) + 2(10)(6) SA = 168 + 100.8 + 120 SA = 388.8 cm2 Feedback A B C D Find the area of each of the six faces and add them to find the total surface area. Be sure to account for all six sides of the prism. Correct! What operation is needed to find the area of each face? PTS: 1 DIF: Average OBJ: 12-4.1 Find the surface areas of rectangular prisms. STA: 7.8 TOP: Find the surface areas of rectangular prisms. KEY: Surface area | Prisms 22. ANS: B Sample: 15 mm 4 mm 4.4 mm Find the area of each of the six faces. Add these together to find the total surface area. SA = 2(4.4)(4) + 2(4)(15) + 2(4.4)(15) SA = 35.2 + 120 + 132 SA = 287.2 mm2 Feedback A B C D What operation is needed to find the area of each face? Correct! Find the area of each of the six faces and add them to find the total surface area. Be sure to account for all six sides of the prism. PTS: 1 DIF: Average OBJ: 12-4.1 Find the surface areas of rectangular prisms. STA: 7.8 TOP: Find the surface areas of rectangular prisms. KEY: Surface area | Prisms SHORT ANSWER 23. ANS: congruent The two hexagons have the same size and shape. They are congruent figures. PTS: 1 DIF: Basic OBJ: 13-6.1 Determine congruence and similarity. STA: 6.15 TOP: Determine congruence and similarity. KEY: Congruent | Similar 24. ANS: neither The two triangles do not have the same size or the same shape. They are neither congruent nor similar. PTS: 1 DIF: Average OBJ: 13-6.1 Determine congruence and similarity. STA: 6.15 TOP: Determine congruence and similarity. KEY: Congruent | Similar 25. ANS: similar The two octagons have the same shape but different sizes. They are similar figures. PTS: 1 DIF: Average OBJ: 13-6.1 Determine congruence and similarity. STA: 6.15 TOP: Determine congruence and similarity. KEY: Congruent | Similar 26. ANS: 24 cm2 Use the formula A = bh. A = 6(4) A = 24 cm2 PTS: 1 DIF: Basic OBJ: 14-1.1 Find the areas of parallelograms. STA: 6.13a | 6.13b TOP: Find the areas of parallelograms. KEY: Area | Parallelograms 27. ANS: 42 unit2 Use the formula A = bh. A = 6(7) A = 42 unit2 PTS: 1 DIF: Average OBJ: 14-1.1 Find the areas of parallelograms. STA: 6.13a | 6.13b TOP: Find the areas of parallelograms. KEY: Area | Parallelograms 28. ANS: 155.6 yd2 Use the formula A = bh. A = 24.7(6.3) A = 155.61 yd2 PTS: 1 DIF: Average OBJ: 14-1.1 Find the areas of parallelograms. STA: 6.13a | 6.13b TOP: Find the areas of parallelograms. KEY: Area | Parallelograms 29. ANS: 80 ft2 Use the formula PTS: 1 STA: 6.13a 30. ANS: 21 unit2 Use the formula PTS: 1 STA: 6.13a . DIF: Average OBJ: 14-2.1 Find the areas of triangles. TOP: Find the areas of triangles. KEY: Area | Triangles . DIF: Average OBJ: 14-2.1 Find the areas of triangles. TOP: Find the areas of triangles. KEY: Area | Triangles 31. ANS: 32.8 m2 Use the formula PTS: 1 STA: 6.13a 32. ANS: 28 unit2 Use the formula . DIF: Average OBJ: 14-2.1 Find the areas of triangles. TOP: Find the areas of triangles. KEY: Area | Triangles . PTS: 1 STA: 6.13a 33. ANS: 9 mi2 Use the formula DIF: Average OBJ: 14-2.1 Find the areas of triangles. TOP: Find the areas of triangles. KEY: Area | Triangles PTS: 1 STA: 6.13a 34. ANS: 53.5 cm2 Use the formula DIF: Basic OBJ: 14-2.1 Find the areas of triangles. TOP: Find the areas of triangles. KEY: Area | Triangles PTS: 1 STA: 6.13a 35. ANS: 560 mm2 Use the formula DIF: Average OBJ: 14-2.1 Find the areas of triangles. TOP: Find the areas of triangles. KEY: Area | Triangles PTS: 1 STA: 6.13a 36. ANS: DIF: Average OBJ: 14-2.1 Find the areas of triangles. TOP: Find the areas of triangles. KEY: Area | Triangles . . . in2 Use the formula PTS: 1 STA: 6.13a 37. ANS: 50.2 km2 Sample: . DIF: Average OBJ: 14-2.1 Find the areas of triangles. TOP: Find the areas of triangles. KEY: Area | Triangles 6 ft Use the formula PTS: 1 STA: 6.15 | 6.16 38. ANS: 35.2 cm2 Sample: . The radius is one half the diameter. DIF: Basic OBJ: 14-3.1 Find the areas of circles. TOP: Find the areas of circles. KEY: Area | Circles 4.6 ft Use the formula . PTS: 1 STA: 6.15 | 6.16 39. ANS: 275.8 mm3 Sample: DIF: Average OBJ: 14-3.1 Find the areas of circles. TOP: Find the areas of circles. KEY: Area | Circles 13 ft 4 ft 5 ft Use the formula V = Bh. V = (5)(4)(13) V = 260 ft3 PTS: 1 DIF: Average OBJ: 14-5.1 Find the volume of rectangular prisms. TOP: Find the volume of rectangular prisms. KEY: Volume | Prisms 40. ANS: 430 mm2 Sample: 13 ft 5 ft 9 ft Find the area of each of the six faces. Add these together to find the total surface area. SA = 2(9)(5) + 2(5)(13) + 2(9)(13) SA = 90 + 130 + 234 SA = 454 ft2 PTS: 1 DIF: Basic OBJ: 14-6.1 Find the surface areas of rectangular prisms. STA: 6.15 TOP: Find the surface areas of rectangular prisms. KEY: Surface area | Prisms ESSAY 41. ANS: a. 90 in2 Use the surface area formula. SA = 2(6)(3) + 2(3)(3) + 2(6)(3) SA = 36 + 18 + 36 SA = 90 in2 b. 54 in3 Use the formula V = Bh. V = (6)(3)(3) V = 54 in3 c. All reasonably drawn prisms should be accepted. PTS: 1 DIF: Advanced OBJ: 14-7.1 Solve problems and show solutions. TOP: Solve problems and show solutions. KEY: Problem solving | Solutions