Question

Construct a rhombus ABCD, when AB = 5 cm and ∠A = 120°.

Answer 1

Given:

• Side AB = 5 cm
• Angle ∠A = 120°

Steps of construction:

1. Draw a line segment AB = 5 cm.
2. At point A, construct an angle of 120° (∠DAB = 120°).
3. From point A along the line making the 120° angle with AB, cut off a length equal to AB (5 cm). Mark this point as D.
4. At point B, construct a line segment BC = 5 cm making an angle of 60° with AB since adjacent angles in a rhombus are supplementary and sides are equal.
5. Join points C and D to complete rhombus ABCD.

ABCD is the required rhombus with side 5 cm and ∠A = 120°.

Note: Since all sides in a rhombus are equal, all sides will be 5 cm. Also, in a rhombus opposite angles are equal and adjacent angles are supplementary, so ∠B = 60° here.

For precise steps with angles at corners B and possibly constructing point C the following method from an example can be adapted:

• Draw AB = 5 cm.
• At A, construct ∠DAB = 120°.
• From A along this angle, mark AD = 5 cm.
• At B, construct ∠ABC = 60° and mark BC = 5 cm.
• Join CD to complete the rhombus.

Thus, ABCD is the required rhombus with given side and angle.