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Standardized Test Practice - Cumulative, Chapters 1-11 or 1. What is the value of x in the figure below? Since length cannot be negative, x = 7. The correct choice is B. ANSWER: B A5 B7 C8 D 10 SOLUTION: The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two segments. The length of this altitude is the geometric mean between the lengths of these two segments. 2. Which of the following is not a property of parallelograms? F The opposite angles of a parallelogram are congruent. G The opposite sides of a parallelogram are congruent. H The consecutive angles of a parallelogram are supplementary. J The consecutive angles of a parallelogram are complementary. SOLUTION: The consecutive angles of a parallelogram are supplementary, not complementary. So, the statement in option J is incorrect. Therefore, the correct choice is J. ANSWER: J 3. What is the area of the triangle below? Round your answer to the nearest tenth if necessary. To factor this polynomial we are looking for factors of whose sum is –14. Factors Sum of factors 24, –49 –25 28, –42 –14 2 A 152.8 in B 159.2 in2 2 C 164.5 in D 171.9 in2 SOLUTION: We need to determine the length of the base of the triangle. Use the tangent ratio to find the left part of the base b 1 and use the Pythagorean Theorem to find the right part of the base b 2. or eSolutions Manual - Powered by Cognero Since length cannot be negative, x = 7. The correct choice is B. Page 1 Use the tangent ratio to find the left part of the base b 1 and use the Pythagorean Theorem to find the right Standardized Test Practice - Cumulative, Chapters 1-11 part of the base b 2. The area of the triangle is about 171.9 square inches. Therefore, the correct choice is D. ANSWER: D 6. GRIDDED RESPONSE Suppose two similar rectangles have a scale factor of 3:5. The perimeter of the smaller rectangle is 21 millimeters. What is the perimeter of the larger rectangle? Express your answer in millimeters. SOLUTION: The ratio of the perimeters of two rectangles is same as the ratio of their sides. Let x be the perimeter of the larger rectangle. The perimeter of the larger rectangle is 35 mm. The area of the triangle is about 171.9 square inches. Therefore, the correct choice is D. ANSWER: 35 7. Copy the circles below on a sheet of paper and draw the common tangents, if any exist. ANSWER: D 6. GRIDDED RESPONSE Suppose two similar rectangles have a scale factor of 3:5. The perimeter of the smaller rectangle is 21 millimeters. What is the perimeter of the larger rectangle? Express your answer in millimeters. SOLUTION: SOLUTION: The ratio of the perimeters of two rectangles is same as the ratio of their sides. Let x be the perimeter of the larger rectangle. Draw the two circles and use a straight edge to look for lines that are tangent to both circles. The easiest to find are the lines tangent to the outside of both. The perimeter of the larger rectangle is 35 mm. eSolutions Manual - Powered by Cognero ANSWER: 35 Page 2 Draw the two and -use a straight edge to look1-11 Standardized Testcircles Practice Cumulative, Chapters for lines that are tangent to both circles. The easiest to find are the lines tangent to the outside of both. 9. Copy the figure and point D. Then use a ruler to draw the image of the figure under a dilation with center D and a scale factor of 2. SOLUTION: The more difficult lines to find are the tangents that cross between the circles. There should be 4 common tangents. ANSWER: There should be 4 common tangents. 9. Copy the figure and point D. Then use a ruler to draw the image of the figure under a dilation with center D and a scale factor of 2. eSolutions Manual - Powered by Cognero Use a ruler to draw guidelines from D to each of the corners of the rectangle. Now measure the distance from each corner to D, and plot the new corners twice this distance along the corresponding lines. Connect the corners to draw the scaled figure. ANSWER: 11. GRIDDED RESPONSE What is the area of the parallelogram below? Express your answer in square feet. Round to the nearest whole number if necessary. Page 3 b. What is the total area of the figure? c. Explain how the areas of the squares model the Pythagorean Theorem. Standardized Test Practice - Cumulative, Chapters 1-11 SOLUTION: a. The area of the triangle is 11. GRIDDED RESPONSE What is the area of the parallelogram below? Express your answer in square feet. Round to the nearest whole number if necessary. The area of the squares are: SOLUTION: Each pair of opposite sides and opposite angles of a parallelogram are congruent. We have a right triangle with an acute angles of 65° and a hypotenuse of 9 ft. b. The total area of the figure is the sum of the areas of the squares and the triangle: 30 + 25 + 144 + 169 2 The area of a parallelogram is the product of the base b and height h. = 368 m . c. The area of each square represents the square of 2 2 a side of a right triangle. They show that a + b = The area of the parallelogram is about 106 square feet. c since 25 + 144 = 169. ANSWER: 106 12. Use the figure below to answer each question. 2 ANSWER: a. 144 m2, 169 m2, 25 m2, 30 m2 2 b. 368 m c. Sample answer: The area of each square represents the square of a side of a right triangle. 2 2 2 They show that a + b = c since 25 + 144 = 169. a. Find the area of each square and the area of the triangle. b. What is the total area of the figure? c. Explain how the areas of the squares model the Pythagorean Theorem. SOLUTION: a. The area of the triangle is eSolutions Manual - Powered by Cognero Page 4