Question

If you are given AB = 5 cm, BC = 6 cm, CD = 7 cm, DA = 6 cm and $\angle$ABC=${60}^{\circ }$. What is the property of the quadrilateral constructed?

• A. A unique quadrilateral is formed
• B. Quadrilateral can't be constructed
• C. The quadrilateral constructed is not unique
• D. Quadrilateral drawn is a kite

Answer 1

The correct option is A

A unique quadrilateral is formed

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 intersect 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 $\angle$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= ${60}^{\circ }$.