Ch. 6: Parallelograms, Rhombus, and Rectangles Possible or Impossible for the described quadrilateral to be a parallelogram…

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Ch. 6: Parallelograms, Rhombus, and Rectangles Possible or Impossible for the described quadrilateral to be a parallelogram…

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?

Impossible If one diagonal bisects two angles, then the figures is a rhombus. A rhombus has 4 congruent sides.

Question 2: Possible/Impossible Each diagonal is 15 cm long and one angle of the quadrilateral has measure 45.

Impossible If diagonals or a parallelogram are congruent, the quadrilateral is a rectangle, but a rectangle has four right angles

Question 3: Possible/Impossible The diagonals are congruent, perpendicular and bisect each other.

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.

Question 4: Possible/Impossible Each diagonal of a parallelogram is 3 cm long and two opposite sides are 2 cm long

Possible Yes, congruent diagonals in a parallelogram mean that the figure is a rectangle with two opposite sides 2 cm. long.

Question 5: Possible/Impossible A diagonal of a parallelogram bisects an angle and has side lengths of 4 and 2.

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.

Question 6: Possible/Impossible A parallelogram has a 90 degree angle and diagonals that are perpendicular to each other?

Possible Perpendicular diagonals and right angle could be a square

Question 7: Possible/ Impossible The parallelogram has congruent diagonals and one angle of 60 degrees.

Impossible A parallelogram with congruent diagonals is a rectangle with four right angles.

Question 8: Possible/Impossible The parallelogram has perpendicular diagonals and four right angles.

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.