Construct a quadrilateral ABCD in which AB = BC = 6 cm, AD = DC = 4.5 cm and ∠B = 120°.
Steps of construction:
Step I: Draw AB = 6 cm .
Step II: Construct ABC = 120°.
Step III : With B as the centre and radius 6 cm, cut off BC = 6 cm .
Now, we can see that AC is about 10 . 3 cm which is greater than AD + CD = 4 . 5 + 4 . 5 = 9 cm .
We know that sum of the lengths of two sides of triangle is always greater than the third side but here, the sum of AD and CD is less than AC .
So, construction of the given quadrilateral is not possible .