If you are given AB = 5 cm, BC = 6 cm, CD = 7 cm, DA = 6 cm and ∠ABC = 60∘, is it possible to draw the quadrilateral ABCD?
Yes
Step 1: Draw BC = 6 cm.
Step 2: At B, draw ∠ABC=60∘. Along that angle make an arc of 5 cm and mark it as point A.
Step 3: From A, draw an arc of 6 cm.
Step 4: From C, draw an arc of 7 cm such that it intersects the arc made from A. Mark the point of intersection as D.
Step 5: Join ABCD to complete the quadrilateral.
Is this quadrilateral unique? Yes, it is.
If we move it keeping all the angles constant ∠ABC will change. Thus, there is only one quadrilateral ABCD with AB = 5 cm, BC = 6 cm, CD = 7 cm, BA = 6 cm, ∠ABC = 60∘.