Question

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.

Answer 1

Answer: The answer is 1, 2 and 4.

Step-by-step explanation:

(1) The quadrilateral with congruent diagonals but no angle is a right angle is an ISOSCELES TRAPEZOID. So, this will not be a parallelogram.

(2) The quadrilateral with two consecutive congruent sides and is not a rhombus is a KITE. So, this will not be a parallelogram

(3) A quadrilateral with each diagonal 3 cm long and two opposite sides 2 cm long will be a RECTANGLE. So, this will be a parallelogram.

(4) A quadrilateral with two opposite angles as right angles is not a rectangle will be a KITE. so, this will also be not a parallelogram.

(5) A quadrilateral in which one diagonal is a perpendicular bisector of the other will be a SQUARE. So, this will be a parallelogram.

Thus, (1), (2) and (4) are the correct options.