Question

Each of the following statements describes a quadrilateral. Which of the quadrilaterals are NOT parallelograms? (Pick 3)

Quadrilateral 1: The diagonals are congruent, but the quadrilateral has no right angles.
Quadrilateral 2: Two consecutive sides are congruent, but the figure is not a rhombus.
Quadrilateral 3: Each diagonal is 3 cm long, and two opposite sides are 2 cm long.
Quadrilateral 4: Two opposite angles are right angles, but the quadrilateral is not a rectangle.
Quadrilateral 5: One diagonal is a perpendicular bisector of the other.

Answer 1

Options: Quadrilateral 1: The diagonals are congruent, but the quadrilateral has no right angles.

Quadrilateral 2: Two consecutive sides are congruent, but the figure is not a rhombus.

Quadrilateral 4: Two opposite angles are right angles, but the quadrilateral is not a rectangle.

Explanation:

In a quadrilateral, the two sides are parallel to each other. This means that the two opposite sides are always equal. In a quadrilateral, the two sides are opposite and equal. In addition, one diagonal is perpendicular bisector of the other. This is true for all the quadrilaterals particularly parallelograms.

In the analysis of the factors above, the options 1, 2 and 4 do not apply.

Answer 2

Quadrilaterals 1, 2 and 4 does not represents a parallelogram.

Explanation:

We know that, a parallelogram is a simple quadrilateral that have two opposite sides congruent.

Now, according to the options:

1. A parallelogram does not have congruent diagonals without having right angles.

2. A parallelogram does not have consecutive sides equal without being a rhombus.

3. A rectangle is a parallelogram which have both the diagonals of equal length. So, this quadrilateral might represents a rectangle, which is a parallelogram.

4. No two opposite angles of a parallelogram are right angles without the quadrilateral being a rectangle.

5. A rhombus is a parallelogram which have both the diagonals bisecting each other perpendicularly. So, this quadrilateral might represents a rhombus, which is a parallelogram.

Hence, we see that options 1, 2 and 4 does not represents a parallelogram.