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Lesson 1: Measurement and Geometry Directions: Read each question carefully and then choose the best answer. Use the diagram below to answer question 1. Use the pictures below to answer question 3. 3. Which pair of code symbols is representative of a rotation? A. 1. What is the total area of both triangular fins of the rocket? A. B. C. D. 54 square feet 108 square feet 216 square feet 270 square feet 2. The garden club put in two rotating sprinklers, each of which waters a circular area of 10 meters in diameter. What is the approximate total area that the two sprinklers will water? J. K. L. M. 78.5 square meters 157 square meters 314 square meters 628 square meters ACES Mathematics: Geometry Workbook B. C. D. Use the picture below to answer question 4. 4. How many buckets of sand will it take to fill the sandbox below if each bucket contains 2 cubic meters of sand? J. K. L. M. 12 13 16 32 1 Lesson 2: Principles of Geometry I Directions: Read each question carefully and then choose the best answer. 1. What is the perimeter of a rhombus with one side that is 5 inches long? A. B. C. D. 15 inches 20 inches 25 inches 30 inches 3. Triangles ABC and DEF are similar. If AB = 4, BC = 2, AC = 5, and DE = 3, what is the perimeter of triangle DEF? B A 2. In the figure below, a triangle is inscribed in a parallelogram. The base of the triangle and the base of the parallelogram are equal. If the area of the parallelogram is 16, what is the area of the triangle? J. K. L. M. C E D F A. 8 B. C. 10 11 D. 16 1 4 7 8 8 10 12 It cannot be determined. ACES Mathematics: Geometry Workbook 2 Lesson 3: Principles of Geometry II Directions: Read each question carefully and then choose the best answer. 1. Which letter has line symmetry? A. B. C. D. F H J P 2. In the figure below, a black triangle is completely contained but not inscribed in a rectangle as shown. If the area of the rectangle is 20, which of the following must be true? 3. The rectangle below is divided into four triangles by its two diagonals. The dimensions of the rectangle are 14 inches by 8 inches. What is the area of the black triangle? A. B. C. D. 14 square inches 28 square inches 42 square inches 56 square inches Note: The figure is not drawn to scale. J. K. L. M. The area of the triangle is more than 20. The triangle must be irregular. The area of the triangle is less than 10. The perimeter of the rectangle is less than 18. ACES Mathematics: Geometry Workbook 3 Lesson 4: Principles of Geometry III Directions: Read each question carefully and then choose the best answer. 1. Which of the letters below has rotational symmetry? A. B. C. D. E H L Q 2. In the figure below, l1 is parallel to l2 and l3 is parallel to l4. The obtuse angle formed by l1 and l4 measures 140º, as shown in the diagram. Line segment BC bisects ABD . l3 C l4 3. A large-scale map uses the figure shown above, which is made up of a square and an isosceles triangle sharing one side, to represent houses in the community. The height of the triangle is ½ the height of the square. If the square in the diagram has sides of 1 inch, what is the area, in square inches, of the entire figure? A. 1 square inch D A B. 140º B l1 l2 C. D. What is the value of ABC ? J. K. L. M. 40º 70º 120º 140º ACES Mathematics: Geometry Workbook 1 square inches 4 1 1 square inches 2 1 2 square inches 4. The length of the third side of any triangle must be greater than J. the length of either of the other two sides. K. the product of the lengths of the other two sides. L. the sum of the lengths of the other two sides. M. the difference between the lengths of the other two sides. 4 Lesson 5: Problem Solving with Geometry I Directions: Read each question carefully and then choose the best answer. Hint: You may find it helpful to create a coordinate grid on a piece of graph paper and plot the points identified in the problems. 1. A circle plotted on a coordinate grid has its center at (0, 0). The radius of the circle is 4. Through which of the following points does the circumference of the circle pass? A. B. C. D. (2, 2) (–4, 0) (4, 4) (4, –4) 2. A triangle plotted on a coordinate grid has vertices at coordinates (4, 1), (12, 1), and (4, 4). What is the area of the triangle? J. K. L. M. J. K. L. M. 6 9 12 18 ACES Mathematics: Geometry Workbook 12 16 24 48 5. Square S and right triangle T share a side, as shown in the diagram below. If the area of triangle T is 6 square inches, what is the area of square S? 8 12 24 48 3. A triangle plotted on a coordinate grid has vertices at coordinates (0, 0), (3, 3), and (6, 0). What is the area of the triangle? A. B. C. D. 4. A rhombus on a coordinate grid has vertices at coordinates (0, 0), (3, 4), (6, 0), and (3, –4). What is the area of the rhombus? S T 3 in. A. B. C. D. 4 square inches 6 square inches 8 square inches 16 square inches 5 Lesson 6: Problem Solving with Geometry II Directions: Read each question carefully and then choose the best answer. Hint: You may find it helpful to create a coordinate grid on a piece of graph paper and plot the points identified in the problems. 1. Line segment AB has endpoints at (–2, –2) and (6, 4). What is the midpoint of this line segment? 3. What is the area of a quadrilateral with vertices at points (–5, –1), (–2, 3), (6, –1), and (–2, –5)? A. B. C. D. A. B. C. D. (1, 2) (2, 1) (–2, 4) (6, –2) 2. A triangle plotted on a coordinate grid has vertices at coordinates (2, 4), (14, 4), and (14, 9). What is the area, in square units, of the triangle? J. K. L. M. 13 30 60 126 ACES Mathematics: Geometry Workbook 10 11 30 44 4. What is the perimeter of a quadrilateral with vertices at points (–5, –1), (–2, 3), (6, –1), and (–2, –5)? J. K. L. M. 52 5 54 5 10 4 5 10 8 5 6 Lesson 7: Problem Solving with Geometry III Directions: Read each question carefully and then choose the best answer. Hint: You may find it helpful to create a coordinate grid on a piece of graph paper and plot the points identified in the problems. 1. What is the area of a triangle with vertices at (–2, 5), (–2, –1), and (3, –1)? 4. What is the midpoint of a line segment with endpoints (–8, –6) and (–1, –6)? A. B. C. D. J. K. L. M. 5 10 15 30 2. What is the perimeter of a triangle with vertices at (–1, 1), (–1, –5), and (2, –5)? J. K. L. M. 9 10 2 12 25 2 93 5 (–3.5, –6) (–4.5, –6) (–3.5, –3) (–4.5, –3) 5. What is the area of a quadrilateral with vertices at points (–3, 0), (0, 4), (3, 0), and (0, –4)? A. B. C. D. 6 12 18 24 3. What is the area of a triangle with vertices at (2, 5), (8, 5), and (2, 3)? 6. What is the perimeter of a quadrilateral with vertices at points (–3, 0), (0, 4), (3, 0), and (0, –4)? A. B. C. D. J. K. L. M. 6 9 15 18 ACES Mathematics: Geometry Workbook 48 24 20 14 7 Lesson 8: Circles Directions: Read each question carefully and then choose the best answer. 1. The drawing below shows an isosceles triangle with one vertex at the center of the circle and the other two vertices on the circumference of the circle. If the length of each leg of the triangle is 2, what is the area of the circle? A. B. C. D. 3. The radius of circle A is twice the radius of circle B. The area of circle A is how many times larger than the area of circle B? A. B. C. D. 2 4 8 It cannot be determined. 4. The diagram below shows two circles, each with a radius of 2. The circles are tangent to each other. Each is inscribed in the rectangle. 6 4 2 A B 2. Chords w, x, y, and z transect circle C as shown in the diagram below. Which chord is longest? w What is the area of the rectangle? x C J. K. L. M. y z w x y z ACES Mathematics: Geometry Workbook J. K. L. M. 4 8 16 32 8 Lesson 9: Angle and Distance Measures Directions: Read each question carefully and then choose the best answer. 1. In triangle ABC below, side AB < side BC < side AC. Which answer choice gives the correct order of the angle values a, b, and c? 3. An isosceles right triangle has a hypotenuse of 6 2 . What is the area of the triangle? A. B. C. D. B bº aº cº A A. B. C. D. C 18 36 72 144 Use the figure below to answer question 4. a<b<c b<c<a c<b<a c<a<b C yº xº 2. What is the sum of the interior angles of the polygon shown below? yº xº A yº B D 4. In the figure, line segments AB and CD meet to form two right angles. What is the value of x – y? J. K. L. M. 360º 540º 720º 900º ACES Mathematics: Geometry Workbook J. K. L. M. 0 15 30 45 9 Lesson 10: Coordinate Geometry Directions: Read each question carefully and then choose the best answer. Use the coordinate grid below to answer questions 1 and 2. Hint: To answer questions 3 and 4, you may find it helpful to create a coordinate grid on a piece of graph paper and plot the points identified in the questions. 3. Point Z has coordinates (5, 9). If Z is reflected across the y-axis, then translated down 7 units, what are the coordinates of the resulting point? 1. The coordinates of point A are (1, 1) and the coordinates of point B are (7, 9). What is the slope of AB? A. B. C. D. –1 3 4 1 4 3 2. What is the length of AB? J. K. L. M. A. B. C. D. (–2, 2) (–5, 2) (–5, –2) (–5, –16) 4. If point Z (5, 9) is reflected across the y-axis and the result is reflected across the x-axis, what are the coordinates of the resulting point? J. K. L. M. (–5, –9) (–9, –5) (5, –9) (–9, 5) 2 10 14 18 ACES Mathematics: Geometry Workbook 10 Lesson 11: Theorems with Geometry I Directions: Read each question carefully and then choose the best answer. 1. If l1 is parallel to l2, which angles are congruent in the diagram below? a l1 A. B. C. D. d b e l2 c A. B. C. D. 3. Which parts of two triangles must be congruent in order to show that the two triangles are entirely congruent? f a and b b and c a and d d and f one side two angles one side and one angle two sides and the angle at which those sides meet 4. Side BC of rectangle ABCD is congruent to side EF of rectangle EFGH. If ABCD and EFGH are similar rectangles, what is the perimeter of rectangle EFGH? 2. In triangle ABC below, a 2 b 2 c 2 only if 6 A A 3 c b B D C J. K. L. M. a B ACB = 90º AC = BC ABC and CAB are supplementary ABC = CAB ACES Mathematics: Geometry Workbook J. K. L. M. C E F H G 6 9 12 18 11 Lesson 12: Theorems with Geometry II Directions: Read each question carefully and then choose the best answer. 3. In the figure below, l1 is parallel to l2. What is the value of x? A C B x l1 F x ( ) 5 H G 1. Triangles ABC and FGH are similar triangles with corresponding parts as shown in the diagram. ABC is equal to which angle in triangle FGH? A. B. C. D. FGH GHF HFG A. B. C. D. 30 90 120 150 4. In the figure below, which two angles must have equal values? No angle in triangle FGH is equal to ABC . a f e 2. Two parallelograms must be similar if they are both J. K. L. M. l2 rectangles. trapezoids. squares. rhombuses. ACES Mathematics: Geometry Workbook J. K. L. M. d b c a and b a and c a and d a and f 12 Lesson 13: Trigonometry I Directions: Read each question carefully and then choose the best answer. Hint: The sine ratio of an acute angle in a right triangle equals the length of the side opposite the angle divided by the length of the hypotenuse. In the right triangle below the sine ratio of angle x is 0.5. Refer to the triangle to answer questions 1 and 2. 3. The figure pictured below is a right triangle. Which is the best approximation of the sine ratio of angle a? 1. If the length of the hypotenuse is 10, what is the length of the side opposite angle x? aº 13 12 xº A. B. C. D. 2.5 5 7.5 10 2. If the length of the side 3 opposite angle x is 7 , what is 4 the length of the hypotenuse of the triangle? J. 3 K. 10 L. 15 M. 22 7 8 1 2 ACES Mathematics: Geometry Workbook 5 A. B. C. D. 0.38 0.92 2.4 2.6 4. A right triangle has sides that are 3, 4, and 5 inches long. Which could be the sine ratio of one of the acute angles of the triangle? J. K. L. M. 0.25 0.4 0.6 0.95 13 Lesson 14: Trigonometry II Directions: Read each question carefully and then choose the best answer. 1. In right triangle ABC below, tan 0.65 and BC = 20. What is the length of AB? Use the figure below to answer questions 3 and 4. In the figure below, EFG is a right triangle with length EF = 24 and length FG = 10. A E B C A. B. C. D. 13 12 10 8 2. In right triangle ABC below, cos 0.80 and BC has a length of 8. What is the length of AC? F G 3. Which of the following is the closest approximation of cos? A A. B. C. D. 0.92 0.5 0.42 0.38 B J. K. L. M. C 8 9 10 16 ACES Mathematics: Geometry Workbook 4. tan = J. K. L. M. 0.42 0.92 1.1 2.4 14 Lesson 15: Trigonometry III Directions: Read each question carefully and then choose the best answer. 1. If ABC is a right triangle with sides AB = 3, BC = 4, and AC = 5, then sin = 3. A wire is attached to the ground and to the top of a telephone pole, as shown in the diagram below. A pole B A. B. C. D. C 0.4 0.6 0.75 0.8 2. In an isosceles right triangle, what is the approximate cosine ratio of either acute interior angle? (Hint: 2 1.4 ) J. K. L. M. wire 0.7 0.9 1 1.4 ACES Mathematics: Geometry Workbook If the pole is 18 feet tall and tan2.75, what is the best approximation of the distance from the base of the pole to the place at which the wire meets the ground? A. B. C. D. 4.3 feet 6.5 feet 9 feet 49.5 feet 15