#$&* course MTH 152 Time: 2:43 PMDate: 8/6
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Given Solution: GOOD STUDENT SOLUTION: This statement is true. A parallelogram is a quadrilateral with two pairs of parallel sides and a rhombus is a parallelogram with all sides having equal length. All sides of a square have equal length. If a square were not a rhombus then all sides would not be of equal length. It is not true that a rhombus must be a square. The angles of a rhombus do not have to be right angles, while the angles of a square do. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): - Redirected my thinking to the congruency of angles/length of sides rather than shape. ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q Query 9.2.10 Consider the statement: 'A parallelogram must be rectangle and a rectangle must be parallelogram ' Is the statement true or false and why? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: - False, because: - A parallelogram is a quadrilateral that has two pairs of parallel sides, whose lengths are not necessarily congruent. - A rectangle is a quadrilateral whose sides are all parallel but not necessarily of equal length that resembles the rules of a square, who must be of congruent 90 deg angles. - If the angles of a rectangle are not all 90 degs, then it becomes a parallelogram. - That said, all rectangles are parallelograms, but not all parallelograms are rectangles. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: A parallelogram is a quadrilateral having two pairs of parallel sides. A rectangle is a parallelogram which includes a pair of adjacent sides which meet at a right angle. A rectangle is a parallelogram but a parallelogram is not necessarily a rectangle, so the statement is false. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): - Headache. I don’t know how many times I had to retype “parallelogram.” I pretty much got the point where I have it copied so I can just CTRL+V to keep from losing my mind. More to the point, though, it is in fact concrete that a rectangle/square is a “fixed” shape so that if any of the angles diverge from 90 degs, it is no longer a square? ------------------------------------------------ Self-critique Rating: See my comment above.
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Given Solution: The curve is closed: If you start from any point on the curve, and continue to follow the curve, you end up where you started. The curve is not simple, but intersects itself ('crosses over' itself) at three points. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): - What would define a lemniscate as? I would say it would be both simple and closed, because it only crosses itself once, and may end at where the symbol began.
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Given Solution: The region inside is convex because the line segment connecting any two points is completely inside the figure. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q Query 9.2.48 Consider the triangle ABC. Angle A is 30 degrees more than angle B, which in turn equals angle C What are the measures of the three angles? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: - I let ‘x’ denote the approximate value of the measurement where A = 30 + x, B = x and C= x. - Once I solve for x, I can definte B and C then added the given sum to get A. - On a Euclidean plane, the three interior angles of a triangle will = 180, so - (30 + x) + x + x = 180 - 3x + 30 = 180 => 3x = 150 = x = 50. - Since B and C were the same value, we see that B = 50 and C = 50. A, however, is 30 degrees more than B, and B is 50. So 50 + 30 = 80. - To check, the cumulative sum of all three interior angles is 180. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: The figure is a triangle so Angle A + Angle B + Angle C = 180 deg. We are also told that angle A is 30 deg more than angle B, so Angle A = Angle B + 30 deg If x is the degree measure of B then angle A has measure x + 30 degrees and angle C has measure x degrees. So we have x + x +30 deg + x = 180 deg 3x + 30 deg = 180 deg 3x = 150 deg x = 50 deg Angle B and Angle C are both equal to x, i.e., to 50 deg. Angle A = 50 deg + 30 deg = 80 deg To check, 80 + 50 + 50 = 180. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q Query Add comments on any surprises or insights you experienced as a result of this assignment. There were no really big surprises. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!