Question

Construct a rhombus ABCD, when AC = 6.5 cm, ∠DAB = 60°.

Answer 1

Given:

• Rhombus ABCD
• Diagonal AC = 6.5 cm
• Angle ∠DAB = 60°

Steps of construction:

1. Draw the diagonal AC = 6.5 cm.
2. At point A, construct the angle ∠DAB = 60° with AC as one arm of the angle.
3. Since ABCD is a rhombus, all sides are equal. Let the side length be AB = AD = s.
4. Using the angle 60° and diagonal AC, calculate side length AB as follows:
5. In triangle ABD with diagonal AC: Since ∠DAB = 60° and ABCD is a rhombus, diagonals bisect at certain angles, but it is easier to construct:
6. With center A and radius AB to be determined, draw an arc along the 60° ray.
7. With center C and radius AB, draw an arc to intersect the arc from A at point B.
8. Join AB, BC, CD and DA to complete the rhombus.

By drawing diagonal AC = 6.5 cm, constructing a 60° angle at A and using the equality of sides AB and AD, the complete rhombus ABCD is constructed with given AC and ∠DAB = 60°.