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Geometry / Mr. Hansen |
Name: _________________________ |
Check for Understanding (Chapter 8)
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1. |
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(a) |
AB = 6, BC = 8, CA = 10; DE = 3, EF = 4, FD = 5 |
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(b) |
AB = 6, BC = 8, CA = 10; DE = 3, FD = 4, EF = 5 |
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(c) |
AB = 4, BC = 7.5, mÐB = 50; DE = 12, EF = 22.5, mÐE = 150 |
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(d) |
AB = 4, BC = 7.5, mÐB = 50; DE = 12, EF = 22.5, mÐE = 50 |
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(e) |
mÐA = 42, mÐB = 44; mÐE = 42, mÐF = 44 |
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(f) |
mÐA = 42, mÐB = 44; mÐD = 42, mÐE = 44 |
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An office building has floors that are 13 feet apart (12 feet of gap plus 1 foot for the floor itself), except for the ground floor, which has 20 feet of clear space from the ground to the ceiling. A diagonal brace on the exterior of the building runs from one corner on the ground to the opposite corner of the top floor. If the diagonal brace is anchored to each floor with points of attachment spaced at 17-foot intervals (center-to-center) for the upper floors, compute the distance (measured diagonally along a brace) between the ground and the nearest attachment point. (The nearest attachment point would be the point that is midway between the first and second floors.) |
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A woman perches on the edge of a 100m tall building with a clear view of another 100m tall building that is 700m away. Her laser pointer can be adjusted so that she can aim it at any point between the roofline and the base of the other building, along a vertical line segment whose highest point is 700m away from her position. Let P be the peak (nearest corner) of the other building, L be the woman's laser, and B be the base (nearest corner) of the other building. If the woman determines her aimpoint by exactly bisecting angle PLB, how high above ground is her aimpoint on the other building? Assume that the ground is level between the two buildings and that both buildings are rectangular prisms (i.e., boxes). |