| To solve the first three problems, complete the following activity first. Use a protractor to draw a 60-degree angle where one ray measures three inches and the other ray measures six inches. Name the vertex of the angle point A. Name the three-inch segment AC and the six-inch segment AB. Connect endpoints B and C to make a triangle. |
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| 1) True or False. Triangle ABC is a right triangle. |
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| Provide a convincing argument that the conjectures in the next two problems are either true or false. Refer to the given right triangle to help make the explanation. |
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| 4) True or False and Why? Conjecture: If the lengths of all three sides of a right triangle are multiplied by the same number, the new lengths will form another right triangle. |
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| 5) True or False and Why? Conjecture: If the same number is added to or subtracted from each side of a right triangle, the new lengths will form another right triangle. |
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| 6) A wooden flag pole broke seven feet above the ground and fell over touching the ground 24 feet away. What was the original height of the flag pole? (Hint: Make sure to add the lengths of the two broken pieces together for the final step.) |
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| 7) Suppose a steel rail for a railroad track was made in a single length of one mile (5280 ft). Suppose the rail is securely anchored on each end. During the day, as the temperature increases, the steel expands and the rail lengthens by 2 feet. If the rail rises off the ground and forms two right triangles with a common altitude (h), how high off the ground would the rail reach at this maximum point? (a) First give a guess as to how much “h” might be. (b) Using the Pythagorean Theorem calculate, and then state “h”. Round the answer to the nearest tenth and label the answer appropriately. |
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| 9) In words, describe how to find the midpoint (halfway point) between two points in the coordinate plane. |
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| 11) Find the length of segment AB by using the Pythagorean Theorem. Count the units to determine “a” and “b”. State the lengths of a, b, and c. |
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| In the previous two problems, two different methods are used to solve the same problem. Compare the two solutions and then answer the next four questions. |
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| 15) In both problems, the value of 100 was found by doing what? |
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| 16) True or False. The final step for finding the length of segment AB in both problems was taking the square root of 100. |
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| 17) True or False. The expression below may be used to determine the distance formula. |
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| 18) True or False. The Pythagorean Theorem may be rewritten as the expression shown below. |
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| For the next two problems, consider point A(3, 4) and point B(6, 8) on straight line AB. |
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| For the next two problems, consider point C(–2, –4) and point D(3, 5) on straight line CD. |
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| For the next two problems, consider points E(0, 0) and point F(-4, 5) on straight line EF. |
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| For the next two problems, consider points G(–3, –3) and point H(4, 4) on straight line GH. |
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| In the next six problems, the figure below represents two parallel lines cut by a transversal and the angles formed by the intersections. |
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| Trapezoid EFGH has vertices at E(1, 1), F(2, 5), G(6, 5), and H(7, 1). On graph paper, draw trapezoid EFGH two times in two separate coordinate planes. For each of the next two problems, perform each transformation in a separate coordinate plane. Draw the results and list the new ordered pairs of the image. Refer back to the original trapezoid for each problem. (Note: Graph paper is provided in the content section of this unit.) |
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| 37) Translate trapezoid EFGH left 5 and up 2. What are the ordered pairs of the vertices of the image? |
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| 38) Translate trapezoid EFGH right 1 and down 4. What are the ordered pairs of the vertices of the image? |
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| 41) Graph the equations and make a statement about the change in the graphs when the coefficient of “x” gets larger. |
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| 42) Before CJ buys the tent shown in the ad below, he wants to make sure that it is as roomy as his old tent. If the average person needs at least 40 cubic feet of space, how many people could fit in the tent? (Notice that this company calculates the volume of the tent by using the given formula. You may want to compare the results of that formula with V = Bh.) |
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| 43) Explain the solution to the previous problem. |
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| 44) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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| No offline activities found |
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