Question

ABCD is a quadrilateral with angle a=80° b=40° c=140° d=100°
1.is ABCD a trapezium?
2.is ABCD a parallelogram?
justify your answer

Answer 1

GIVEN :

ABCD is a quadrilateral with $\angle A=80^\circ$ $\angle B=40^\circ$,  $\angle C=140^\circ$ and $\angle D=100^\circ$

TO JUSTIFY :

1. Is ABCD a trapezium

2 Is ABCD a parallelogram

SOLUTION :

Given ABCD is a quadrilateral with $\angle A=80^\circ$ $\angle B=40^\circ$,  $\angle C=140^\circ$ and $\angle D=100^\circ$

From the definition of quadrilateral, the given quadrilateral ABCD is a trapezium.

For :

Quadrilateral ABCD is a trapezium because properties of parallelogram does not exists.

• The parallel sides are called bases.
• The other two non-parallel sides are called legs.
• If the two non-parallel sides are equal and form equal angles at one of the bases, the trapezium is an isosceles trapezium.

• Trapezium is a quadrilateral with one pair of opposite parallel sides.

•  Opposite angles of a parallelogram are congruent but in the given quadrliateral ABCD none of the opposite angles are equal.(refer figure)

• 2) The adjacent angles of a parallelogram are suplementary but in the given quadrliateral ABCD its adjacent angles exceeds 180 degree
• The opposite or facing sides of a parallelogram are of equal lengths and their opposite angles are of equal measuring angle.

Hence ABCD quadrilateral is a Trapezium

Answer 2

Answer : this is the right answer