#$&* course MTH 152 4/17 6 021. ``q Query 21*********************************************
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Given Solution: GOOD STUDENT SOLUTION: This statement is true. A parallelogram is a quadrilateral with two pairs of parallel sides and a rhombus is a parallelogram with all sides having equal length. All sides of a square have equal length. If a square were not a rhombus then all sides would not be of equal length. It is not true that a rhombus must be a square. The angles of a rhombus do not have to be right angles, while the angles of a square do. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q Query 9.2.10 Consider the statement: 'A parallelogram must be rectangle and a rectangle must be parallelogram ' • Is the statement true or false and why? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: A parallelogram is a four sided shape with two pairs of parallel sides. A rectangle must always be a four sided shape with two pairs of parallel sides. Therefore, a rectangle must always be a parallelogram. However, much like rhombi cannot always be classified as squares, parallelograms can also not always be classified as rectangles. The sides of a rectangle must always meet at right angle. This is not true for all shapes classified as a parallelogram. Therefore, a parallelogram is not always a rectangle. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q Query 9.2.18 A plane curve is defined by a rubber band with 4 loops. • Is the curve simple, closed, both or neither? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The shape in problem 18 is closed. There is no beginning or end to the circle; it is always a fused shape. The curve is not simple, as it overlaps itself at several different points. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: The curve is closed: If you start from any point on the curve, and continue to follow the curve, you end up where you started. The curve is not simple, but intersects itself ('crosses over' itself) at three points. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q Query 9.2.24 A curve consists of an ellipse. • Is the region inside the curve convex or not, and why? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The area inside is convex because the line segment connecting the points is contained inside the shape. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* 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: In order to find the measure of the three angles, we must keep in mind that the angles of a triangle add up to 180 degrees. We are given the information that angle A is 30 degrees more than angle B, so angle A is equal to angle B+30 degrees. Angle B and angle C have the same length of measurement, so we can create an equation of x+x+30 deg+x+180. We can solve this equation like any other equation. There are three xs on the left side of the equation. This means that we can simplify the equation to 3x+30=180 deg. We can then subtract 30 from each side of the equation, leaving us with 3x=150. When we divide each side of the equation by 3, we find that x is equal to 50. This means that angles B and C are equal to 50, while angle A is equal to 80. When we add each measurement of angle together, we find that we have 180 degrees. This is how we know that our calculations are correct. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q Query Add comments on any surprises or insights you experienced as a result of this assignment. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!