Mathematics
Grade9
Easy

Question

Which of the following is not true about a parallelogram?

  1. AB equals CD
  2. A D ‖ B C
  3. angle C plus angle D equals 180 degree
  4. angle A plus angle C equals 180 degree

hintHint:

Polygon is a two- dimensional closed figure which is consist of three or more-line segments. Each polygon has different properties. One of the polygons is quadrilateral. Quadrilateral is a four-sided polygon with four angles and the sum of all angles of a quadrilateral is 360 degree . Here, we have to find the correct property of the given quadrilateral among the given options.

The correct answer is: angle A plus angle C equals 180 degree


    In the question there is a parallelogram ABCD as shown in the figure.
    Here, we have to find the option which doesn't match with the properties of parallelogram.
    In option a, it is given that AB=CD which is true for a parallelogram. (As in parallelogram two pairs of opposite sides are equal and parallel.)
    In option b, it is given that A D parallel to B C which is true for a parallelogram. (As in parallelogram two pairs of opposite sides are equal and parallel.)
    In option c, it is given that, angle C plus angle D equals 180 degree which is true for a parallelogram. (As in a parallelogram its consecutive angles are supplementary.)
    In option d, it is given that, angle A plus angle C equals 180 degree which is not true for a parallelogram. (As in a parallelogram its consecutive angles are supplementary.)
    So, the option which doesn't match with the properties of parallelogram is d.
    Therefore, the correct option is d, i.e., angle A plus angle C equals 180 degree.

    Parallelogram is a four-sided polygon whose opposite sides are parallel and equal to each other and the opposite angles are equal to each other. The sum of all angles of a parallelogram is 360 degree and sum of two consecutive angles is 180 degree . The diagonals of a parallelogram bisect each other and the angle into two equal halves. Here, we have to use these properties of a parallelogram and solve the given question.

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