Each of the following statements describes a quadrilateral. Which of the quadrilaterals are NOT parallelograms? Choose three.
1: The diagonals are congruent, but the quadrilateral has no right angles.
2: Two consecutive sides are congruent, but the figure is not a rhombus.
3: Each diagonal is 3 cm long, and the two opposite sides are 2 cm long.
4: Two opposite angles are right angles, but the quadrilateral is not a rectangle.
5: One diagonal is a perpendicular bisector of the other.
This question really confuses me. I think I kinda get it, I feel I should choose 2, 4, and 5, but I'm really not sure at all. I don't get it:p Please help? Thanks
To determine which quadrilaterals are not parallelograms, let's analyze each statement:
1: The diagonals are congruent, but the quadrilateral has no right angles.
This describes a rhombus, which is a special type of parallelogram. So, this statement does not specify a quadrilateral that is not a parallelogram.
2: Two consecutive sides are congruent, but the figure is not a rhombus.
Since a rhombus is a special type of parallelogram, this statement implies that the quadrilateral is not a parallelogram.
3: Each diagonal is 3 cm long, and the two opposite sides are 2 cm long.
This describes a kite, which is not a parallelogram. So, this statement specifies a quadrilateral that is not a parallelogram.
4: Two opposite angles are right angles, but the quadrilateral is not a rectangle.
A rectangle is a special type of parallelogram, so this statement does not describe a quadrilateral that is not a parallelogram.
5: One diagonal is a perpendicular bisector of the other.
This describes a rectangle, which is a special type of parallelogram. So, this statement does not specify a quadrilateral that is not a parallelogram.
Based on the analysis above, the three quadrilaterals that are not parallelograms are 2, 3, and 5.
To determine which of the statements describes quadrilaterals that are not parallelograms, we need to understand the properties of parallelograms.
1: The diagonals are congruent, but the quadrilateral has no right angles.
This statement describes a parallelogram. In a parallelogram, opposite sides are parallel and congruent, and opposite angles are congruent. So, statement 1 describes a parallelogram.
2: Two consecutive sides are congruent, but the figure is not a rhombus.
In a rhombus, all four sides are congruent. So, if two consecutive sides are congruent, but the figure is not a rhombus, then the quadrilateral described in statement 2 is not a parallelogram.
3: Each diagonal is 3 cm long, and the two opposite sides are 2 cm long.
This statement does not provide enough information about the angles or the parallelism of the sides. Therefore, we cannot determine if the quadrilateral described in statement 3 is a parallelogram or not.
4: Two opposite angles are right angles, but the quadrilateral is not a rectangle.
A rectangle is a type of parallelogram, so if two opposite angles are right angles, it must be a parallelogram with right angles. Therefore, statement 4 does describe a parallelogram.
5: One diagonal is a perpendicular bisector of the other.
This statement describes a kite, which is not a parallelogram. In a kite, one diagonal is the perpendicular bisector of the other diagonal. Therefore, statement 5 does not describe a parallelogram.
Based on our analysis, the quadrilaterals that are NOT parallelograms are statements 2, 3, and 5.
1: probably a trapezoid
2: Must mean that there are two such congruent sides, not that all pairs are congruent. Might be a trapezoid or a kite.
3: could be a rectangle or trapezoid. Diagonals of a rhombus are not equal.
4: general quadrilateral. Try drawing one
5: kite
Try drawing an example of each.