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.