ABCD is a quadrilateral with angel A =80° angel B =40° angel C = 140° Angel D=100° is ABCD a trapezium .Is ABCD a parallelogram
Answers
Answer:
Step-by-step explanation:
A=80
B=40
C=140
D=100
We know that the sum of all sides of a trapezium is 360
So A+B+C+D=360
80+40+140+100=360
120+240=360
360=360
So A,B,C,D is a trapezium
GIVEN :
ABCD is a quadrilateral with \angle A=80^\circ∠A=80
∘
\angle B=40^\circ∠B=40
∘
, \angle C=140^\circ∠C=140
∘
and \angle D=100^\circ∠D=100
∘
TO JUSTIFY :
1. Is ABCD a trapezium
2 Is ABCD a parallelogram
SOLUTION :
Given ABCD is a quadrilateral with \angle A=80^\circ∠A=80
∘
\angle B=40^\circ∠B=40
∘
, \angle C=140^\circ∠C=140
∘
and \angle D=100^\circ∠D=100
∘
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
