Question

If you are given AB = 5 cm, BC = 6 cm, CD = 7 cm, DA = 6 cm and $\angle$ ABC= ${60}^{\circ }$, can you draw a quadrilateral?

Answer 1

Let us try to draw the quadrilateral:

Step 1: Draw BC = 6 cm.

Step 2: At B, draw an angle = ${60}^{\circ }$. 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 angle length constant $△$ ABC will change. So, there is only one quadrilateral ABCD with AB = 5 cm, BC = 6 cm, CD = 7 cm, BA = 6 cm, $\angle$ ABC= ${60}^{\circ }$.