course Mth 152 yyzð݊assignment #021
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18:55:03 Liberal Arts Mathematics II
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18:55:09 Asst # 21
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18:55:12 03-25-2003
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18:58:03 **** query 9.2.6 sq must be rhombus **** Is the statement true or false and why?
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RESPONSE --> True--A square and a rhombus have four equal sides.
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18:58:23 ** 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. **
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RESPONSE --> Correct answer.
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19:01:22 **** query 9.2.10 parallelogram must be rect and rect must be parallelogram **** Is the statement true or false and why?
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RESPONSE --> False. A rectangle is a parallelogram, but a parallelogram does not have to be a rectangle because a parallelogram does not have to have four right angles like a rectangle.
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19:01:31 ** A rectangle is a parallelogram but a parallelogram is not necessarily a rectangle, so the statement is false. **
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RESPONSE --> Correct answer.
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19:02:11 **** query 9.2.18 rb with 4 loops **** Is the curve simple, closed, both or neither?
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RESPONSE --> Closed.
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19:02:21 This is only a closed curve because its starting point and ending point are the same and it can be drawn without lifting the pencil from the paper. It is not simple because some points are passed through twice.
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RESPONSE --> Correct answer.
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19:17:28 **** query 9.2.24 ellipse **** Is the region inside the curve convex or not, and why?
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RESPONSE --> Yes, the region inside the curve is convex because line segment AB would be completely inside the ellipse.
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19:17:38 The region inside is convex because the line segment connecting any two points is completely inside the figure.
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RESPONSE --> Correct answer.
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19:21:58 **** query 9.2.48 A 30 deg more than B which equals C **** What are the measures of the three angles?
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RESPONSE --> Triangle ABC = 180 deg angle A is x + 30 angle B is x angle C is x x + 30 + x + x = 180 3x + 30 = 180 3x + 30 - 30 = 180 - 30 3x = 150 x = 50 angle A is 80 deg angle B is 50 deg angle C is 50 deg
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19:22:11 Angle A + Angle B + Angle C = 180 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 + x = 180 3x + 30 = 180 3x = 150 x = 50 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.
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RESPONSE --> Correct answer.
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19:23:04 **** What equation did you solve to obtain your answer, and how did you use the solution to determine all angles?
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RESPONSE --> x + 30 + x + x = 180 Angles B and C were equal to x and Angle C was 30 more than x.
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19:23:14 Student Response: The definition for the angle sum of a triangle says the sum of the measures of the angles of any triangle is 180 deg. I used x to represent angles B and C and x + 30 to represent angle A since it is 30 deg higher than the other two. All this equaled 180 deg. I solved for x to get the degree measure of angles B and C and then added 30 on to x to get the degree measure for angle A.
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RESPONSE --> Correct answer.
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19:23:21 **** Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> No surprises.
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