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प्रश्न
Construct a parallelogram ABCD, AC = 8 cm, BD = 6.5 cm, ∠AOB = 60°.
भौमितिक रेखाचित्रे
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उत्तर
Given:
- Parallelogram ABCD
- Diagonal AC = 8 cm
- Diagonal BD = 6.5 cm
- ∠AOB = 60°, where O is the intersection point of the diagonals
Steps of construction:
1. Draw the diagonal AC = 8 cm.
2. Find the midpoint O of AC by constructing its perpendicular bisector.
Since diagonals of a parallelogram bisect each other,
AO = OC
= `8/2`
= 4 cm
3. At point O, construct the angle ∠AOB = 60°.
4. On the line forming angle 60° at O,
Cut segment `OB = (BD)/2`
= `6.5/2`
= 3.25 cm
5. Extend OB through point B to D such that OD = OB = 3.25 cm.
6. Join points A to B, B to C, C to D and D to A, completing the parallelogram ABCD.
ABCD is the parallelogram with diagonals AC = 8 cm, BD = 6.5 cm and the angle between the diagonals ∠AOB = 60° constructed as above.
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