Question

If you are given AB = 5 cm, BC = 6 cm, CD = 7 cm, DA = 6 cm and $\angle ABC$ = ${60}^{\circ }$, is it possible to draw the quadrilateral ABCD?

• A. With measurement of one angle, yes
• B. With measurement of one diagonal, yes
• C. No
• D. Yes

Answer 1

The correct option is D

Yes

Step 1: Draw BC = 6 cm.

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