Geometry SIA #2 Practice Exam

Transcription

1 Class: Date: Geometry SIA #2 Practice Exam Short Answer 1. Justify the last two steps of the proof. Given: RS UT and RT US Prove: RST UTS Proof: 1. RS UT 1. Given 2. RT US 2. Given 3. ST TS 3.? 4. RST UTS 4.? 2. Name the angle included by the sides PN and NM. 1

2 3. What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate? 4. State whether ABC and AED are congruent. Justify your answer. 5. Which triangles are congruent by ASA? 2

3 6. Which two triangles are congruent by ASA? AF bisects EC, and AED FCD. 7. What is the missing reason in the two-column proof? Given: MO bisects PMN and OM bisects PON Prove: PMO NMO Statements Reasons 1. MO bisects PMN 1. Given 2. PMO NMO 2. Definition of angle bisector 3. MO MO 3. Reflexive property 4. OM bisects PON 4. Given 5. POM NOM 5. Definition of angle bisector 6. PMO NMO 6.? 3

4 8. What is the value of x? 9. What is the value of x? 10. What is the value of x? 4

5 11. Find the value of x. The diagram is not to scale. Given: RS ST, m RST 7x 54, m STU 8x 12. Two sides of an equilateral triangle have lengths 2x 2 and 3x 6. Which could be the length of the third side: 10 x or 6x 5? 13. The legs of an isosceles triangle have lengths 2x 4 and x 8. The base has length 5x 2. What is the length of the base? 14. Find the values of x and y. 15. In an A-frame house, the two congruent sides extend from the ground to form a 34 angle at the peak. What angle does each side form with the ground? 16. Find the value of x. The diagram is not to scale. 5

6 17. Find the sum of the measures of the angles of the figure. 18. What is the sum of the angle measures of a 36-gon? 19. The sum of the angle measures of a polygon with s sides is Find s. 20. What is the measure of one angle in a regular 25-gon? 21. A road sign is in the shape of a regular heptagon. What is the measure of each angle on the sign? Round to the nearest tenth. 22. Find the missing values of the variables. The diagram is not to scale. 23. Find the value of x. The diagram is not to scale. 24. The sum of the measures of two exterior angles of a triangle is 255. What is the measure of the third exterior angle? 6

7 25. How many sides does a regular polygon have if each exterior angle measures 20? 26. This jewelry box has the shape of a regular pentagon. It is packaged in a rectangular box as shown here. The box uses two pairs of congruent right triangles made of foam to fill its four corners. Find the measure of the foam angle marked. 27. Use less than, equal to, or greater than to complete this statement: The measure of each exterior angle of a regular 7-gon is the measure of each exterior angle of a regular 5-gon. 28. Use less than, equal to, or greater than to complete this statement: The sum of the measures of the exterior angles of a regular 5-gon, one at each vertex, is the sum of the measures of the exterior angles of a regular 9-gon, one at each vertex. 29. A nonregular hexagon has five exterior angle measures of 55, 60, 69, 57, and 57. What is the measure of the interior angle adjacent to the sixth exterior angle? 30. Find the values of the variables in the parallelogram. The diagram is not to scale. 7

8 31. In the parallelogram, m KLO 69 and m MLO 47. Find m KJM. The diagram is not to scale. 32. In the parallelogram, m QRP 46 and m PRS 50. Find m PQR. The diagram is not to scale. 33. ABCD is a parallelogram. If m CDA 66, then m BCD?. The diagram is not to scale. 34. For the parallelogram, if m 2 5x 28 and m 4 3x 10, find m 3. The diagram is not to scale. 8

9 35. ABCD is a parallelogram. If m DAB 115, then m BCD?. The diagram is not to scale. 36. In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 4x 5, and HE = 2y + 3. Find the values of x and y. The diagram is not to scale. 37. Find AM in the parallelogram if PN =10 and AO = 5. The diagram is not to scale. 38. LMNO is a parallelogram. If NM = x + 15 and OL = 3x + 5, find the value of x and then find NM and OL. 9

10 39. In the figure, the horizontal lines are parallel and AB BC CD. Find JM. The diagram is not to scale. 40. In the figure, the horizontal lines are parallel and AB BC CD. Find KL and FG. The diagram is not to scale. 41. A model is made of a car. The car is 9 feet long and the model is 6 inches long. What is the ratio of the length of the car to the length of the model? 42. The length of a rectangle is inches and the width is 41 inches. What is the ratio, using whole numbers, of 4 the length to the width? 43. Red and grey bricks were used to build a decorative wall. The bricks used in all. How many red bricks were used? number of red bricks number of grey bricks was 5. There were The measure of two complementary angles are in the ratio 1 : 4. What are the degree measures of the two angles? 45. The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 128 feet, what is the length of the rectangle? 46. A salsa recipe uses green pepper, onion, and tomato in the extended ratio 1 : 3 : 9. How many cups of onion are needed to make 117 cups of salsa? 10

11 47. The measures of the angles of a triangle are in the extended ratio 3 : 5 : 7. What is the measure of the smallest angle? What is the solution of each proportion? a m Given the proportion a b 8 15, what ratio completes the equivalent proportion a 8? Are the polygons similar? If they are, write a similarity statement and give the scale factor. 51. The polygons are similar, but not necessarily drawn to scale. Find the value of x You want to draw an enlargement of a design that is printed on a card that is 4 in. by 5 in. You will be drawing this design on an piece of paper that is 8 1 in. by 11 in. What are the dimensions of the largest complete 2 enlargement you can make? 11

12 54. In a diagram of a landscape plan, the scale is 1 cm = 10 ft. In the diagram, the trees are 4.2 centimeters apart. How far apart should the actual trees be planted? 55. In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of 5000 kilometers, what should be the diameter of the drawing of the planet? Find the geometric mean of the pair of numbers and and and What are the values of a and b? 60. Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale. 12

13 61. Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kristen s home and the football field at the exact point where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 2 miles from her home. The football field is 5 miles from the library. a. How far is library from the park? b. How far is the park from the football field? 62. What is the value of x, given that PQ BC? 13

14 63. Plots of land between two roads are laid out according to the boundaries shown. The boundaries between the two roads are parallel. What is the length of Plot 3 along Cheshire Road? 64. What is the value of x to the nearest tenth? 65. An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. A second side of the triangle is 6.9 cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter. 66. Find the length of the missing side. The triangle is not drawn to scale. 14

15 Triangle ABC has side lengths 9, 40, and 41. Do the side lengths form a Pythagorean triple? Explain. 69. Find the length of the missing side. Leave your answer in simplest radical form A grid shows the positions of a subway stop and your house. The subway stop is located at ( 5, 2) and your house is located at ( 9, 9). What is the distance, to the nearest unit, between your house and the subway stop? 72. A triangle has sides of lengths 6, 8, and 10. Is it a right triangle? Explain. 73. A triangle has sides of lengths 24, 62, and 67. Is it a right triangle? Explain. 74. A triangle has side lengths of 14 cm, 48 cm, and 50 cm. Classify it as acute, obtuse, or right. 75. A triangle has side lengths of 28 in, 4 in, and 31 in. Classify it as acute, obtuse, or right. 15

16 76. In triangle ABC, A is a right angle and m B 45. Find BC. If your answer is not an integer, leave it in simplest radical form. 77. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form. 78. Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth. 79. Find the value of the variable. If your answer is not an integer, leave it in simplest radical form. 80. The area of a square garden is 242 m 2. How long is the diagonal? 16

17 81. Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 10 inches long. What is the side length of each piece? 82. The length of the hypotenuse of a triangle is 4. Find the perimeter. 83. Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form. 84. Not drawn to scale A piece of art is in the shape of an equilateral triangle with sides of 13 in. Find the area of the piece of art. Round your answer to the nearest tenth. 87. A sign is in the shape of a rhombus with a 60 angle and sides of 9 cm long. Find its area to the nearest tenth. 88. A conveyor belt carries supplies from the first floor to the second floor, which is 24 feet higher. The belt makes a 60 angle with the ground. How far do the supplies travel from one end of the conveyor belt to the other? Round your answer to the nearest foot. If the belt moves at 75 ft/min, how long, to the nearest tenth of a minute, does it take the supplies to move to the second floor? 17

18 89. Find the missing value to the nearest hundredth. 90. Find the missing value to the nearest hundredth. 91. Find the missing value to the nearest hundredth. 92. Write the tangent ratios for Y and Z. 93. Write the tangent ratios for P and Q. 18

19 94. Write the ratios for sin A and cos A. 95. Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth Find the value of x. Round to the nearest tenth. 19

20 Viola drives 170 meters up a hill that makes an angle of 6 with the horizontal. To the nearest tenth of a meter, what horizontal distance has she covered? 102. Find the value of x. Round to the nearest degree. 20

21 103. Find the value of x to the nearest degree What is the description of 2 as it relates to the situation shown? Find the value of x. Round the length to the nearest tenth

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23 111. To approach the runway, a pilot of a small plane must begin a 9 descent starting from a height of 1125 feet above the ground. To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach? 112. Find the area. The figure is not drawn to scale

24 The area of a parallelogram is 420 cm 2 and the height is 35 cm. Find the corresponding base Find the area of a polygon with the vertices of ( 4, 5), ( 1, 5), (4, 3), and ( 4, 3). Find the area of the trapezoid. Leave your answer in simplest radical form

25 121. What is the area of the kite? 122. A kite has diagonals 9.2 ft and 8 ft. What is the area of the kite? 123. Find the area of the rhombus. Leave your answer in simplest radical form Find the area of the rhombus. 25

26 The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second. The figures are not drawn to scale The widths of two similar rectangles are 16 cm and 14 cm. What is the ratio of the perimeters? Of the areas? 127. The area of a regular octagon is 35 cm 2. What is the area of a regular octagon with sides three times as long? 128. The triangles are similar. The area of the larger triangle is 1589 ft 2. Find the area of the smaller triangle to the nearest whole number Find the similarity ratio and the ratio of perimeters for two regular pentagons with areas of 49 cm 2 and 169 cm 2. Find the area of the circle. Leave your answer in terms of

27 A team in science class placed a chalk mark on the side of a wheel and rolled the wheel in a straight line until the chalk mark returned to the same position. The team then measured the distance the wheel had rolled and found it to be 35 cm. To the nearest tenth, what is the area of the wheel? 133. Find the area of the figure to the nearest tenth Find the area of a sector with a central angle of 180 and a diameter of 5.6 cm. Round to the nearest tenth The area of sector AOB is ft 2. Find the exact area of the shaded region. 27

28 136. A jewelry store buys small boxes in which to wrap items that they sell. The diagram below shows one of the boxes. Find the lateral area and the surface area of the box to the nearest whole number Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number

29 Find the surface area of the cylinder in terms of Find the surface area of the cylinder to the nearest whole number The radius of the base of a cylinder is 39 in. and its height is 33 in.. Find the surface area of the cylinder in terms of. 29

30 Find the surface area of the pyramid shown to the nearest whole number Find the slant height x of the pyramid shown, to the nearest tenth. 30

31 146. Find the slant height of the cone to the nearest whole number. Find the volume of the given prism. Round to the nearest tenth if necessary

32 Find the volume of the cylinder in terms of Find the volume of the square pyramid shown. Round to the nearest tenth if necessary

33 Find the volume of a square pyramid with base edges of 48 cm and a slant height of 26 cm Find the volume of the cone shown as a decimal rounded to the nearest tenth

34 157. Find the volume of the oblique cone shown. Round to the nearest tenth Find the volume of the oblique cone shown in terms of. Find the surface area of the sphere with the given dimension. Leave your answer in terms of radius of 60 m 160. diameter of 14 cm 161. Find the surface area of a sphere with a circumference of 13 mm. Round to the nearest tenth A balloon has a circumference of 11 cm. Use the circumference to approximate the surface area of the balloon to the nearest square centimeter. 34

35 Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit The volume of a sphere is 5000 m 3. What is the surface area of the sphere to the nearest square meter? 166. The volume of a sphere is 1928 m 3. What is the surface area of the sphere to the nearest tenth? 167. Are the two figures similar? If so, give the similarity ratio of the smaller figure to the larger figure. 35

36 Find the similarity ratio of a prism with the surface area of 81 m 2 to a similar prism with the surface area of 361 m Find the similarity ratio of a cube with volume 216 ft 3 to a cube with volume 1000 ft If the scale factor of two similar solids is 3 : 14, what is the ratio of their corresponding areas? What is the ratio of their corresponding volumes? 173. A glass vase weighs 0.22 lb. How much does a similarly shaped vase of the same glass weigh if each dimension is 6 times as large? 174. The surface areas of two similar solids are 384 yd 2 and 1057 yd 2. The volume of the larger solid is 1795 yd 3. What is the volume of the smaller solid? 36

37 Geometry SIA #2 Practice Exam Answer Section SHORT ANSWER 1. ANS: Reflexive Property of ; SSS PTS: 1 DIF: L3 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: Prove two triangles congruent using the SSS and SAS Postulates STA: MA.912.G.4.3 MA.912.G.4.6 TOP: 4-2 Problem 1 Using SSS KEY: SSS reflexive property proof 2. ANS: N PTS: 1 DIF: L2 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: Prove two triangles congruent using the SSS and SAS Postulates STA: MA.912.G.4.3 MA.912.G.4.6 TOP: 4-2 Problem 2 Using SAS KEY: angle DOK: DOK 1 3. ANS: AC BD PTS: 1 DIF: L4 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: Prove two triangles congruent using the SSS and SAS Postulates STA: MA.912.G.4.3 MA.912.G.4.6 TOP: 4-2 Problem 2 Using SAS KEY: SAS reasoning 4. ANS: yes, by either SSS or SAS PTS: 1 DIF: L3 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: Prove two triangles congruent using the SSS and SAS Postulates STA: MA.912.G.4.3 MA.912.G.4.6 TOP: 4-2 Problem 3 Identifying Congruent Triangles KEY: SSS SAS reasoning 5. ANS: VTU and ABC PTS: 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: Prove two triangles congruent using the ASA Postulate and the AAS Theorem STA: MA.912.G.4.3 MA.912.G.4.6 MA.912.G.8.5 TOP: 4-3 Problem 1 Using ASA KEY: ASA DOK: DOK 1 6. ANS: ADE and FDC PTS: 1 DIF: L4 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: Prove two triangles congruent using the ASA Postulate and the AAS Theorem STA: MA.912.G.4.3 MA.912.G.4.6 MA.912.G.8.5 TOP: 4-3 Problem 1 Using ASA KEY: ASA vertical angles 1

38 7. ANS: ASA Postulate PTS: 1 DIF: L3 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: Prove two triangles congruent using the ASA Postulate and the AAS Theorem STA: MA.912.G.4.3 MA.912.G.4.6 MA.912.G.8.5 TOP: 4-3 Problem 2 Writing a Proof Using ASA 8. ANS: 71 KEY: ASA proof PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles OBJ: Use and apply properties of isosceles and equilateral triangles STA: MA.912.G.4.1 TOP: 4-5 Problem 2 Using Algebra KEY: isosceles triangle Converse of Isosceles Triangle Theorem Triangle Angle-Sum Theorem 9. ANS: 68 PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles OBJ: Use and apply properties of isosceles and equilateral triangles STA: MA.912.G.4.1 TOP: 4-5 Problem 2 Using Algebra KEY: isosceles triangle Isosceles Triangle Theorem Triangle Angle-Sum Theorem word problem 10. ANS: PTS: 1 DIF: L3 REF: 4-5 Isosceles and Equilateral Triangles OBJ: Use and apply properties of isosceles and equilateral triangles STA: MA.912.G.4.1 TOP: 4-5 Problem 2 Using Algebra KEY: Isosceles Triangle Theorem Triangle Angle-Sum Theorem isosceles triangle 11. ANS: 14 PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral Triangles OBJ: Use and apply properties of isosceles and equilateral triangles STA: MA.912.G.4.1 TOP: 4-5 Problem 2 Using Algebra KEY: Isosceles Triangle Theorem isosceles triangle problem solving Triangle Angle-Sum Theorem 12. ANS: 10 x only PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral Triangles OBJ: Use and apply properties of isosceles and equilateral triangles STA: MA.912.G.4.1 TOP: 4-5 Problem 2 Using Algebra KEY: equilateral triangle word problem problem solving DOK: DOK 3 2

39 13. ANS: 18 PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral Triangles OBJ: Use and apply properties of isosceles and equilateral triangles STA: MA.912.G.4.1 TOP: 4-5 Problem 2 Using Algebra KEY: isosceles triangle Isosceles Triangle Theorem word problem problem solving DOK: DOK ANS: x 90, y 43 PTS: 1 DIF: L3 REF: 4-5 Isosceles and Equilateral Triangles OBJ: Use and apply properties of isosceles and equilateral triangles STA: MA.912.G.4.1 TOP: 4-5 Problem 2 Using Algebra KEY: angle bisector isosceles triangle 15. ANS: 73 PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles OBJ: Use and apply properties of isosceles and equilateral triangles STA: MA.912.G.4.1 TOP: 4-5 Problem 3 Finding Angle Measures KEY: Isosceles Triangle Theorem isosceles triangle Triangle Angle-Sum Theorem word problem problem solving 16. ANS: x 23 PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral Triangles OBJ: Use and apply properties of isosceles and equilateral triangles STA: MA.912.G.4.1 TOP: 4-5 Problem 3 Finding Angle Measures KEY: Isosceles Triangle Theorem isosceles triangle 17. ANS: 900 PTS: 1 DIF: L2 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: Find the sum of the measures of the interior angles of a polygon STA: MA.912.G.2.1 MA.912.G.2.2 TOP: 6-1 Problem 1 Finding a Polygon Angle Sum KEY: sum of angles of a polygon DOK: DOK ANS: 6120 PTS: 1 DIF: L3 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: Find the sum of the measures of the interior angles of a polygon STA: MA.912.G.2.1 MA.912.G.2.2 TOP: 6-1 Problem 1 Finding a Polygon Angle Sum KEY: sum of angles of a polygon DOK: DOK 1 3

40 19. ANS: 16 PTS: 1 DIF: L3 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: Find the sum of the measures of the interior angles of a polygon STA: MA.912.G.2.1 MA.912.G.2.2 TOP: 6-1 Problem 1 Finding a Polygon Angle Sum KEY: sum of angles of a polygon 20. ANS: PTS: 1 DIF: L3 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: Find the sum of the measures of the interior angles of a polygon STA: MA.912.G.2.1 MA.912.G.2.2 TOP: 6-1 Problem 2 Using the Polygon Angle-Sum KEY: sum of angles of a polygon equilateral Corollary to the Polygon Angle-Sum Theorem regular polygon 21. ANS: PTS: 1 DIF: L3 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: Find the sum of the measures of the interior angles of a polygon STA: MA.912.G.2.1 MA.912.G.2.2 TOP: 6-1 Problem 2 Using the Polygon Angle-Sum KEY: sum of angles of a polygon equilateral Corollary to the Polygon Angle-Sum Theorem regular polygon 22. ANS: x = 114, y = 56 PTS: 1 DIF: L3 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: Find the sum of the measures of the interior angles of a polygon STA: MA.912.G.2.1 MA.912.G.2.2 TOP: 6-1 Problem 3 Using the Polygon Angle-Sum Theorem KEY: exterior angle Polygon Angle-Sum Theorem 23. ANS: 45 PTS: 1 DIF: L4 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: Find the sum of the measures of the interior angles of a polygon STA: MA.912.G.2.1 MA.912.G.2.2 TOP: 6-1 Problem 3 Using the Polygon Angle-Sum Theorem KEY: Polygon Angle-Sum Theorem 24. ANS: 105 PTS: 1 DIF: L3 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: Find the sum of the measures of the exterior angles of a polygon STA: MA.912.G.2.1 MA.912.G.2.2 TOP: 6-1 Problem 4 Finding an Exterior Angle Measure KEY: angle triangle exterior angle Polygon Angle-Sum Theorem 4

41 25. ANS: 18 sides PTS: 1 DIF: L3 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: Find the sum of the measures of the exterior angles of a polygon STA: MA.912.G.2.1 MA.912.G.2.2 TOP: 6-1 Problem 4 Finding an Exterior Angle Measure KEY: sum of angles of a polygon 26. ANS: 36 PTS: 1 DIF: L4 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: Find the sum of the measures of the exterior angles of a polygon STA: MA.912.G.2.1 MA.912.G.2.2 TOP: 6-1 Problem 4 Finding an Exterior Angle Measure KEY: angle pentagon Polygon Angle-Sum Theorem 27. ANS: less than PTS: 1 DIF: L4 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: Find the sum of the measures of the exterior angles of a polygon STA: MA.912.G.2.1 MA.912.G.2.2 TOP: 6-1 Problem 4 Finding an Exterior Angle Measure KEY: sum of angles of a polygon 28. ANS: equal to PTS: 1 DIF: L3 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: Find the sum of the measures of the exterior angles of a polygon STA: MA.912.G.2.1 MA.912.G.2.2 TOP: 6-1 Problem 4 Finding an Exterior Angle Measure KEY: sum of angles of a polygon 29. ANS: 118 PTS: 1 DIF: L4 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: Find the sum of the measures of the exterior angles of a polygon STA: MA.912.G.2.1 MA.912.G.2.2 TOP: 6-1 Problem 4 Finding an Exterior Angle Measure KEY: hexagon angle exterior angle 30. ANS: x 29, y 49, z 102 PTS: 1 DIF: L4 REF: 6-2 Properties of Parallelograms OBJ: Use relationships among sides and angles of parallelograms STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 MA.912.G.4.5 TOP: 6-2 Problem 1 Using Consecutive Angles KEY: parallelogram opposite angles consecutive angles transversal 5

42 31. ANS: 116 PTS: 1 DIF: L4 REF: 6-2 Properties of Parallelograms OBJ: Use relationships among sides and angles of parallelograms STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 MA.912.G.4.5 TOP: 6-2 Problem 1 Using Consecutive Angles 32. ANS: 84 KEY: parallelogram angles PTS: 1 DIF: L4 REF: 6-2 Properties of Parallelograms OBJ: Use relationships among sides and angles of parallelograms STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 MA.912.G.4.5 TOP: 6-2 Problem 1 Using Consecutive Angles 33. ANS: 114 KEY: parallelogram angles PTS: 1 DIF: L2 REF: 6-2 Properties of Parallelograms OBJ: Use relationships among sides and angles of parallelograms STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 MA.912.G.4.5 TOP: 6-2 Problem 1 Using Consecutive Angles DOK: DOK ANS: 163 PTS: 1 DIF: L4 REF: 6-2 Properties of Parallelograms OBJ: Use relationships among sides and angles of parallelograms STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 MA.912.G.4.5 TOP: 6-2 Problem 1 Using Consecutive Angles KEY: algebra parallelogram opposite angles consecutive angles 35. ANS: 115 KEY: parallelogram consecutive angles PTS: 1 DIF: L2 REF: 6-2 Properties of Parallelograms OBJ: Use relationships among sides and angles of parallelograms STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 MA.912.G.4.5 TOP: 6-2 Problem 1 Using Consecutive Angles KEY: parallelogram opposite angles DOK: DOK 1 6

43 36. ANS: x = 3, y = 2 PTS: 1 DIF: L3 REF: 6-2 Properties of Parallelograms OBJ: Use relationships among diagonals of parallelograms STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 MA.912.G.4.5 TOP: 6-2 Problem 3 Using Algebra to Find Lengths KEY: transversal diagonal parallelogram algebra 37. ANS: 5 PTS: 1 DIF: L2 REF: 6-2 Properties of Parallelograms OBJ: Use relationships among diagonals of parallelograms STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 MA.912.G.4.5 TOP: 6-2 Problem 3 Using Algebra to Find Lengths KEY: parallelogram diagonal DOK: DOK ANS: x = 5, NM = 20, OL = 20 PTS: 1 DIF: L2 REF: 6-2 Properties of Parallelograms OBJ: Use relationships among sides and angles of parallelograms STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 MA.912.G.4.5 TOP: 6-2 Problem 3 Using Algebra to Find Lengths 39. ANS: 24 KEY: parallelogram algebra PTS: 1 DIF: L3 REF: 6-2 Properties of Parallelograms OBJ: Use relationships among sides and angles of parallelograms STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 MA.912.G.4.5 TOP: 6-2 Problem 4 Using Parallel Lines and Transversals 40. ANS: KL = 7.6, FG = 5.1 KEY: transversal parallel lines PTS: 1 DIF: L2 REF: 6-2 Properties of Parallelograms OBJ: Use relationships among sides and angles of parallelograms STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 MA.912.G.4.5 TOP: 6-2 Problem 4 Using Parallel Lines and Transversals DOK: DOK ANS: 18 : 1 KEY: parallel lines transversal PTS: 1 DIF: L3 REF: 7-1 Ratios and Proportions OBJ: Write ratios and solve proportions TOP: 7-1 Problem 1 Writing a Ratio KEY: ratio word problem 7

44 42. ANS: 26 : 17 PTS: 1 DIF: L3 REF: 7-1 Ratios and Proportions OBJ: Write ratios and solve proportions TOP: 7-1 Problem 1 Writing a Ratio KEY: ratio 43. ANS: 125 PTS: 1 DIF: L3 REF: 7-1 Ratios and Proportions OBJ: Write ratios and solve proportions TOP: 7-1 Problem 2 Dividing a Quantity into a Given Ratio KEY: ratio word problem 44. ANS: 18 and 72 PTS: 1 DIF: L3 REF: 7-1 Ratios and Proportions OBJ: Write ratios and solve proportions TOP: 7-1 Problem 2 Dividing a Quantity into a Given Ratio KEY: ratio 45. ANS: 48 feet PTS: 1 DIF: L3 REF: 7-1 Ratios and Proportions OBJ: Write ratios and solve proportions TOP: 7-1 Problem 2 Dividing a Quantity into a Given Ratio KEY: ratio perimeter 46. ANS: 27 PTS: 1 DIF: L3 REF: 7-1 Ratios and Proportions OBJ: Write ratios and solve proportions TOP: 7-1 Problem 3 Using an Extended Ratio KEY: ratio extended ratio word problem 47. ANS: 36 PTS: 1 DIF: L3 REF: 7-1 Ratios and Proportions OBJ: Write ratios and solve proportions TOP: 7-1 Problem 3 Using an Extended Ratio KEY: ratio extended ratio interior angles of a triangle 48. ANS: 9 PTS: 1 DIF: L3 REF: 7-1 Ratios and Proportions OBJ: Write ratios and solve proportions TOP: 7-1 Problem 4 Solving a Proportion KEY: proportion Cross-Product Property DOK: DOK 1 8

45 49. ANS: 21 PTS: 1 DIF: L2 REF: 7-1 Ratios and Proportions OBJ: Write ratios and solve proportions TOP: 7-1 Problem 4 Solving a Proportion KEY: proportion Cross-Product Property DOK: DOK ANS: b 15 PTS: 1 DIF: L2 REF: 7-1 Ratios and Proportions OBJ: Write ratios and solve proportions TOP: 7-1 Problem 5 Writing Equivalent Proportions KEY: proportion Properties of Proportions equivalent proportions 51. ANS: The polygons are not similar. PTS: 1 DIF: L4 REF: 7-2 Similar Polygons OBJ: Identify and apply similar polygons STA: MA.912.G.2.3 TOP: 7-2 Problem 2 Determining Similarity KEY: similar polygons 52. ANS: 29.5 PTS: 1 DIF: L3 REF: 7-2 Similar Polygons OBJ: Identify and apply similar polygons STA: MA.912.G.2.3 TOP: 7-2 Problem 3 Using Similar Polygons KEY: corresponding sides proportion 53. ANS: in. by in. PTS: 1 DIF: L4 REF: 7-2 Similar Polygons OBJ: Identify and apply similar polygons STA: MA.912.G.2.3 TOP: 7-2 Problem 4 Using Similarity KEY: similar polygons word problem 54. ANS: 42 feet PTS: 1 DIF: L3 REF: 7-2 Similar Polygons OBJ: Identify and apply similar polygons STA: MA.912.G.2.3 TOP: 7-2 Problem 5 Use a Scale Drawing KEY: scale drawing proportions word problem 9

46 55. ANS: 10 millimeters PTS: 1 DIF: L3 REF: 7-2 Similar Polygons OBJ: Identify and apply similar polygons STA: MA.912.G.2.3 TOP: 7-2 Problem 5 Use a Scale Drawing KEY: scale drawing proportions word problem 56. ANS: 2 15 PTS: 1 DIF: L4 REF: 7-4 Similarity in Right Triangles OBJ: Find and use relationships in similar triangles STA: MA.912.G.2.3 MA.912.G.4.6 MA.912.G.5.2 MA.912.G.5.4 MA.912.G.8.3 TOP: 7-4 Problem 2 Finding the Geometric Mean 57. ANS: KEY: geometric mean proportion PTS: 1 DIF: L3 REF: 7-4 Similarity in Right Triangles OBJ: Find and use relationships in similar triangles STA: MA.912.G.2.3 MA.912.G.4.6 MA.912.G.5.2 MA.912.G.5.4 MA.912.G.8.3 TOP: 7-4 Problem 2 Finding the Geometric Mean 58. ANS: 12 KEY: geometric mean proportion PTS: 1 DIF: L2 REF: 7-4 Similarity in Right Triangles OBJ: Find and use relationships in similar triangles STA: MA.912.G.2.3 MA.912.G.4.6 MA.912.G.5.2 MA.912.G.5.4 MA.912.G.8.3 TOP: 7-4 Problem 2 Finding the Geometric Mean 59. ANS: a = 8, b = 2 17 KEY: geometric mean proportion PTS: 1 DIF: L3 REF: 7-4 Similarity in Right Triangles OBJ: Find and use relationships in similar triangles STA: MA.912.G.2.3 MA.912.G.4.6 MA.912.G.5.2 MA.912.G.5.4 MA.912.G.8.3 TOP: 7-4 Problem 3 Using the Corollaries KEY: corollaries of the geometric mean proportion 60. ANS: 7 3 PTS: 1 DIF: L3 REF: 7-4 Similarity in Right Triangles OBJ: Find and use relationships in similar triangles STA: MA.912.G.2.3 MA.912.G.4.6 MA.912.G.5.2 MA.912.G.5.4 MA.912.G.8.3 TOP: 7-4 Problem 3 Using the Corollaries KEY: corollaries of the geometric mean proportion

47 61. ANS: 10 miles; 35 miles PTS: 1 DIF: L4 REF: 7-4 Similarity in Right Triangles OBJ: Find and use relationships in similar triangles STA: MA.912.G.2.3 MA.912.G.4.6 MA.912.G.5.2 MA.912.G.5.4 MA.912.G.8.3 TOP: 7-4 Problem 4 Finding a Distance KEY: corollaries of the geometric mean multi-part question word problem 62. ANS: 6 PTS: 1 DIF: L2 REF: 7-5 Proportions in Triangles OBJ: Use the Side-Splitter Theorem and the Triangles Angle-Bisector Theorem STA: MA.912.G.2.3 MA.912.G.4.5 MA.912.G.4.6 TOP: 7-5 Problem 1 Using the Side-Splitter Theorem 63. ANS: yards KEY: Side-Splitter Theorem PTS: 1 DIF: L3 REF: 7-5 Proportions in Triangles OBJ: Use the Side-Splitter Theorem and the Triangles Angle-Bisector Theorem STA: MA.912.G.2.3 MA.912.G.4.5 MA.912.G.4.6 TOP: 7-5 Problem 2 Finding a Length KEY: corollary of Side-Splitter Theorem word problem 64. ANS: 14.4 PTS: 1 DIF: L3 REF: 7-5 Proportions in Triangles OBJ: Use the Side-Splitter Theorem and the Triangles Angle-Bisector Theorem STA: MA.912.G.2.3 MA.912.G.4.5 MA.912.G.4.6 TOP: 7-5 Problem 3 Using the Triangle-Angle-Bisector Theorem KEY: Triangle-Angle-Bisector Theorem 65. ANS: 8.3 cm, 5.8 cm PTS: 1 DIF: L4 REF: 7-5 Proportions in Triangles OBJ: Use the Side-Splitter Theorem and the Triangles Angle-Bisector Theorem STA: MA.912.G.2.3 MA.912.G.4.5 MA.912.G.4.6 TOP: 7-5 Problem 3 Using the Triangle-Angle-Bisector Theorem KEY: Triangle-Angle-Bisector Theorem DOK: DOK 3 11

48 66. ANS: 10 PTS: 1 DIF: L2 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: Use the Pythagorean Theorem and its converse STA: MA.912.G.5.1 MA.912.G.5.4 MA.912.G.8.3 TOP: 8-1 Problem 1 Finding the Length of the Hypotenuse KEY: Pythagorean Theorem leg hypotenuse DOK: DOK ANS: 7 PTS: 1 DIF: L3 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: Use the Pythagorean Theorem and its converse STA: MA.912.G.5.1 MA.912.G.5.4 MA.912.G.8.3 TOP: 8-1 Problem 2 Finding the Length of a Leg KEY: Pythagorean Theorem leg hypotenuse DOK: DOK ANS: Yes, they form a Pythagorean triple; and 9, 40, and 41 are all nonzero whole numbers. PTS: 1 DIF: L3 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: Use the Pythagorean Theorem and its converse STA: MA.912.G.5.1 MA.912.G.5.4 MA.912.G.8.3 TOP: 8-1 Problem 1 Finding the Length of the Hypotenuse KEY: Pythagorean Theorem leg hypotenuse DOK: DOK ANS: 113 m PTS: 1 DIF: L3 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: Use the Pythagorean Theorem and its converse STA: MA.912.G.5.1 MA.912.G.5.4 MA.912.G.8.3 TOP: 8-1 Problem 1 Finding the Length of the Hypotenuse KEY: Pythagorean Theorem leg hypotenuse DOK: DOK ANS: 203 m PTS: 1 DIF: L3 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: Use the Pythagorean Theorem and its converse STA: MA.912.G.5.1 MA.912.G.5.4 MA.912.G.8.3 TOP: 8-1 Problem 2 Finding the Length of a Leg KEY: Pythagorean Theorem leg hypotenuse DOK: DOK 1 12

49 71. ANS: 8 PTS: 1 DIF: L3 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: Use the Pythagorean Theorem and its converse STA: MA.912.G.5.1 MA.912.G.5.4 MA.912.G.8.3 TOP: 8-1 Problem 3 Finding Distance KEY: Pythagorean Theorem leg hypotenuse word problem problem solving 72. ANS: yes; PTS: 1 DIF: L3 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: Use the Pythagorean Theorem and its converse STA: MA.912.G.5.1 MA.912.G.5.4 MA.912.G.8.3 TOP: 8-1 Problem 4 Identifying a Right Triangle KEY: Pythagorean Theorem Pythagorean triple DOK: DOK ANS: no; PTS: 1 DIF: L3 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: Use the Pythagorean Theorem and its converse STA: MA.912.G.5.1 MA.912.G.5.4 MA.912.G.8.3 TOP: 8-1 Problem 4 Identifying a Right Triangle KEY: Pythagorean Theorem Pythagorean triple DOK: DOK ANS: right PTS: 1 DIF: L3 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: Use the Pythagorean Theorem and its converse STA: MA.912.G.5.1 MA.912.G.5.4 MA.912.G.8.3 TOP: 8-1 Problem 5 Classifying a Triangle KEY: right triangle obtuse triangle acute triangle DOK: DOK ANS: obtuse PTS: 1 DIF: L3 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: Use the Pythagorean Theorem and its converse STA: MA.912.G.5.1 MA.912.G.5.4 MA.912.G.8.3 TOP: 8-1 Problem 5 Classifying a Triangle KEY: right triangle obtuse triangle acute triangle DOK: DOK 1 13

50 76. ANS: 11 2 ft PTS: 1 DIF: L2 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 1 Finding the Length of the Hypotenuse DOK: DOK ANS: 8 2 KEY: special right triangles PTS: 1 DIF: L3 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 2 Finding the Length of a Leg KEY: special right triangles hypotenuse leg DOK: DOK ANS: x = 9.9, y = 7 PTS: 1 DIF: L4 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 2 Finding the Length of a Leg KEY: special right triangles hypotenuse leg DOK: DOK ANS: PTS: 1 DIF: L3 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 2 Finding the Length of a Leg KEY: special right triangles hypotenuse leg DOK: DOK ANS: 22 m PTS: 1 DIF: L4 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 3 Finding Distance KEY: special right triangles diagonal 14

51 81. ANS: 5 2 PTS: 1 DIF: L3 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 3 Finding Distance KEY: special right triangles word problem 82. ANS: PTS: 1 DIF: L4 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 4 Using the Length of One Side DOK: DOK ANS: 6 3 PTS: 1 DIF: L2 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 4 Using the Length of One Side KEY: special right triangles leg hypotenuse 84. ANS: x = 30, y = 10 3 PTS: 1 DIF: L3 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 4 Using the Length of One Side KEY: special right triangles leg hypotenuse 85. ANS: x = 17 3, y = 34 PTS: 1 DIF: L3 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 4 Using the Length of One Side KEY: special right triangles leg hypotenuse KEY: special right triangles perimeter 15

52 86. ANS: 73.2 in. 2 PTS: 1 DIF: L2 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 5 Applying the 30º-60º-90º Triangle Theorem KEY: area of a triangle word problem problem solving 87. ANS: 70.1 cm 2 PTS: 1 DIF: L3 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 5 Applying the 30º-60º-90º Triangle Theorem KEY: rhombus word problem problem solving 88. ANS: 28 ft; 0.4 min PTS: 1 DIF: L4 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 5 Applying the 30º-60º-90º Triangle Theorem KEY: special right triangles multi-part question word problem problem solving DOK: DOK ANS: PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 3 Using Inverses KEY: angle measure using tangent DOK: DOK ANS: 60 PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 3 Using Inverses KEY: angle measure using cosine DOK: DOK ANS: 4.59 PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 3 Using Inverses KEY: angle measure using sine DOK: DOK 1 16

53 92. ANS: tan Y 3 5 ; tan Z 5 3 PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 1 Writing Trigonometric Ratios KEY: leg adjacent to angle leg opposite angle tangent tangent ratio DOK: DOK ANS: tan P ; tan Q PTS: 1 DIF: L2 REF: 8-3 Trigonometry OBJ: Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 1 Writing Trigonometric Ratios KEY: tangent ratio tangent leg opposite angle leg adjacent to angle DOK: DOK ANS: sin A 3 5, cos A 4 5 PTS: 1 DIF: L2 REF: 8-3 Trigonometry OBJ: Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 1 Writing Trigonometric Ratios KEY: sine cosine sine ratio cosine ratio DOK: DOK ANS: 24.7 PTS: 1 DIF: L2 REF: 8-3 Trigonometry OBJ: Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: side length using tangent tangent tangent ratio 96. ANS: 4 PTS: 1 DIF: L2 REF: 8-3 Trigonometry OBJ: Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: side length using tangent tangent tangent ratio 17

54 97. ANS: 12.5 PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: cosine side length using sine and cosine cosine ratio 98. ANS: 8.1 PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: cosine side length using sine and cosine cosine ratio 99. ANS: 31.4 PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: sine side length using sine and cosine sine ratio 100. ANS: 6.2 PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: sine side length using sine and cosine sine ratio 101. ANS: m PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: cosine word problem side length using sine and cosine problem solving cosine ratio 18

55 102. ANS: 44 PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 3 Using Inverses KEY: inverse of cosine and sine angle measure using sine and cosine cosine 103. ANS: 35 PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 3 Using Inverses KEY: inverse of cosine and sine angle measure using sine and cosine sine 104. ANS: 60 PTS: 1 DIF: L2 REF: 8-3 Trigonometry OBJ: Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 3 Using Inverses KEY: inverse of tangent tangent tangent ratio angle measure using tangent 105. ANS: 2 is the angle of elevation from the radar tower to the airplane. PTS: 1 DIF: L2 REF: 8-4 Angles of Elevation and Depression OBJ: Use angles of elevation and depression to solve problems STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-4 Problem 1 Identifying Angles of Elevation and Depression KEY: angles of elevation and depression DOK: DOK ANS: 8.6 m PTS: 1 DIF: L3 REF: 8-4 Angles of Elevation and Depression OBJ: Use angles of elevation and depression to solve problems STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-4 Problem 2 Using the Angle of Elevation KEY: sine side length using sine and cosine sine ratio 107. ANS: 7.9 ft PTS: 1 DIF: L3 REF: 8-4 Angles of Elevation and Depression OBJ: Use angles of elevation and depression to solve problems STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-4 Problem 2 Using the Angle of Elevation KEY: cosine side length using sine and cosine cosine ratio 19

56 108. ANS: 9.2 cm PTS: 1 DIF: L3 REF: 8-4 Angles of Elevation and Depression OBJ: Use angles of elevation and depression to solve problems STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-4 Problem 2 Using the Angle of Elevation KEY: tangent side length using tangent tangent ratio 109. ANS: m PTS: 1 DIF: L3 REF: 8-4 Angles of Elevation and Depression OBJ: Use angles of elevation and depression to solve problems STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-4 Problem 3 Using the Angle of Depression KEY: sine side length using sine and cosine sine ratio angles of elevation and depression 110. ANS: 10.4 yd PTS: 1 DIF: L3 REF: 8-4 Angles of Elevation and Depression OBJ: Use angles of elevation and depression to solve problems STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-4 Problem 3 Using the Angle of Depression KEY: tangent side length using tangent tangent ratio angles of elevation and depression 111. ANS: 1.4 mi PTS: 1 DIF: L3 REF: 8-4 Angles of Elevation and Depression OBJ: Use angles of elevation and depression to solve problems STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-4 Problem 3 Using the Angle of Depression KEY: side length using sine and cosine word problem problem solving sine angles of elevation and depression sine ratio 112. ANS: cm 2 PTS: 1 DIF: L3 REF: 10-1 Areas of Parallelograms and Triangles OBJ: Find the area of parallelograms and triangles STA: MA.912.G.2.5 MA.912.G.2.7 TOP: 10-1 Problem 1 Finding the Area of a Parallelogram KEY: area parallelogram base height 113. ANS: 1188 in. 2 PTS: 1 DIF: L3 REF: 10-1 Areas of Parallelograms and Triangles OBJ: Find the area of parallelograms and triangles STA: MA.912.G.2.5 MA.912.G.2.7 TOP: 10-1 Problem 1 Finding the Area of a Parallelogram KEY: area parallelogram base height 20

57 114. ANS: 15 yd 2 PTS: 1 DIF: L3 REF: 10-1 Areas of Parallelograms and Triangles OBJ: Find the area of parallelograms and triangles STA: MA.912.G.2.5 MA.912.G.2.7 TOP: 10-1 Problem 3 Finding the Area of a Triangle KEY: triangle area 115. ANS: 5.4 cm 2 PTS: 1 DIF: L3 REF: 10-1 Areas of Parallelograms and Triangles OBJ: Find the area of parallelograms and triangles STA: MA.912.G.2.5 MA.912.G.2.7 TOP: 10-1 Problem 3 Finding the Area of a Triangle KEY: triangle area 116. ANS: 12 cm PTS: 1 DIF: L3 REF: 10-1 Areas of Parallelograms and Triangles OBJ: Find the area of parallelograms and triangles STA: MA.912.G.2.5 MA.912.G.2.7 TOP: 10-1 Problem 2 Finding a Missing Dimension KEY: area base height parallelogram 117. ANS: 44 units 2 PTS: 1 DIF: L4 REF: 10-1 Areas of Parallelograms and Triangles OBJ: Find the area of parallelograms and triangles STA: MA.912.G.2.5 MA.912.G.2.7 TOP: 10-1 Problem 1 Finding the Area of a Parallelogram KEY: area rectangle 118. ANS: 91 cm 2 PTS: 1 DIF: L3 REF: 10-2 Areas of Trapezoids, Rhombuses, and Kites OBJ: Find the area of a trapezoid, rhombus, or kite STA: MA.912.G.2.5 MA.912.G.2.7 TOP: 10-2 Problem 1 Area of a Trapezoid KEY: area trapezoid 119. ANS: 32 3 ft 2 PTS: 1 DIF: L3 REF: 10-2 Areas of Trapezoids, Rhombuses, and Kites OBJ: Find the area of a trapezoid, rhombus, or kite STA: MA.912.G.2.5 MA.912.G.2.7 TOP: 10-2 Problem 2 Finding Area Using a Right Triangle KEY: area trapezoid 21

58 120. ANS: 84 ft 2 PTS: 1 DIF: L3 REF: 10-2 Areas of Trapezoids, Rhombuses, and Kites OBJ: Find the area of a trapezoid, rhombus, or kite STA: MA.912.G.2.5 MA.912.G.2.7 TOP: 10-2 Problem 2 Finding Area Using a Right Triangle KEY: area trapezoid 121. ANS: 90 ft 2 PTS: 1 DIF: L3 REF: 10-2 Areas of Trapezoids, Rhombuses, and Kites OBJ: Find the area of a trapezoid, rhombus, or kite STA: MA.912.G.2.5 MA.912.G.2.7 TOP: 10-2 Problem 3 Finding the Area of a Kite KEY: area kite 122. ANS: 36.8 ft 2 PTS: 1 DIF: L3 REF: 10-2 Areas of Trapezoids, Rhombuses, and Kites OBJ: Find the area of a trapezoid, rhombus, or kite STA: MA.912.G.2.5 MA.912.G.2.7 TOP: 10-2 Problem 3 Finding the Area of a Kite KEY: area kite 123. ANS: 50 3 PTS: 1 DIF: L3 REF: 10-2 Areas of Trapezoids, Rhombuses, and Kites OBJ: Find the area of a trapezoid, rhombus, or kite STA: MA.912.G.2.5 MA.912.G.2.7 TOP: 10-2 Problem 4 Finding the Area of a Rhombus KEY: rhombus diagonal area 124. ANS: 128 m 2 PTS: 1 DIF: L3 REF: 10-2 Areas of Trapezoids, Rhombuses, and Kites OBJ: Find the area of a trapezoid, rhombus, or kite STA: MA.912.G.2.5 MA.912.G.2.7 TOP: 10-2 Problem 4 Finding the Area of a Rhombus KEY: area rhombus 125. ANS: 5 : 6 and 25 : 36 PTS: 1 DIF: L3 REF: 10-4 Perimeters and Areas of Similar Figures OBJ: Find the perimeters and areas of similar polygons STA: MA.912.G.2.3 MA.912.G.2.5 MA.912.G.2.7 MA.912.G.4.4 TOP: 10-4 Problem 1 Finding Ratios in Similar Figures KEY: perimeter area similar figures DOK: DOK 1 22

59 126. ANS: 8 : 7 and 64 : 49 PTS: 1 DIF: L3 REF: 10-4 Perimeters and Areas of Similar Figures OBJ: Find the perimeters and areas of similar polygons STA: MA.912.G.2.3 MA.912.G.2.5 MA.912.G.2.7 MA.912.G.4.4 TOP: 10-4 Problem 1 Finding Ratios in Similar Figures 127. ANS: 315 cm 2 KEY: perimeter area similar figures PTS: 1 DIF: L4 REF: 10-4 Perimeters and Areas of Similar Figures OBJ: Find the perimeters and areas of similar polygons STA: MA.912.G.2.3 MA.912.G.2.5 MA.912.G.2.7 MA.912.G.4.4 TOP: 10-4 Problem 2 Finding Areas Using Similar Figures 128. ANS: 1217 ft 2 KEY: similar figures area PTS: 1 DIF: L3 REF: 10-4 Perimeters and Areas of Similar Figures OBJ: Find the perimeters and areas of similar polygons STA: MA.912.G.2.3 MA.912.G.2.5 MA.912.G.2.7 MA.912.G.4.4 TOP: 10-4 Problem 2 Finding Areas Using Similar Figures 129. ANS: 7 : 13; 7 : 13 KEY: similar figures area PTS: 1 DIF: L3 REF: 10-4 Perimeters and Areas of Similar Figures OBJ: Find the perimeters and areas of similar polygons STA: MA.912.G.2.3 MA.912.G.2.5 MA.912.G.2.7 MA.912.G.4.4 TOP: 10-4 Problem 4 Finding Perimeter Ratios 130. ANS: m 2 KEY: similar figures similarity ratio PTS: 1 DIF: L3 REF: 10-7 Areas of Circles and Sectors OBJ: Find the areas of circles, sectors, and segments of circles STA: MA.912.G.2.7 MA.912.G.6.4 MA.912.G.6.5 TOP: 10-7 Problem 1 Finding the Area of a Circle KEY: area of a circle radius 23