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Published byEmery Hensley Modified over 9 years ago
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Ch. 6: Parallelograms, Rhombus, and Rectangles Possible or Impossible for the described quadrilateral to be a parallelogram…
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Question 1: Possible/Impossible? A diagonal of a parallelogram bisects two angles of the parallelogram. Is it possible for the parallelogram to have sides of lengths 5, 6, 5, and 6?
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Impossible If one diagonal bisects two angles, then the figures is a rhombus. A rhombus has 4 congruent sides.
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Question 2: Possible/Impossible Each diagonal is 15 cm long and one angle of the quadrilateral has measure 45.
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Impossible If diagonals or a parallelogram are congruent, the quadrilateral is a rectangle, but a rectangle has four right angles
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Question 3: Possible/Impossible The diagonals are congruent, perpendicular and bisect each other.
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Possible If diagonals of a parallelogram are congruent, the quadrilateral is a rectangle. It the diagonals of a parallelogram are perpendicular, the quadrilateral is a rhombus, and a rectangle that is a rhombus is a square.
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Question 4: Possible/Impossible Each diagonal of a parallelogram is 3 cm long and two opposite sides are 2 cm long
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Possible Yes, congruent diagonals in a parallelogram mean that the figure is a rectangle with two opposite sides 2 cm. long.
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Question 5: Possible/Impossible A diagonal of a parallelogram bisects an angle and has side lengths of 4 and 2.
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Impossible If a figure is a parallelogram then the angle opposite the bisected angle is also bisected so the figure is a rhombus. A rhombus has 4 congruent sides.
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Question 6: Possible/Impossible A parallelogram has a 90 degree angle and diagonals that are perpendicular to each other?
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Possible Perpendicular diagonals and right angle could be a square
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Question 7: Possible/ Impossible The parallelogram has congruent diagonals and one angle of 60 degrees.
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Impossible A parallelogram with congruent diagonals is a rectangle with four right angles.
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Question 8: Possible/Impossible The parallelogram has perpendicular diagonals and four right angles.
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Possible Perpendicular diagonals means the figure is a rhombus. Four 90 degree angles means that it is a rectangle. Both properties imply it is a square.
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