how to construct a parallelogram in which diagonal ac=7.2cm,bd=5cm and also angle between the diagonals is 30 degree?
You know that the diagonals bisect each other
so construct a 30° angle, make one arm 3.6 and the other 2.5
Extend each arm its own length at the 30° angle.
Join the endpoints to finalize the parallelogram.
To construct a parallelogram with given diagonal lengths and the angle between diagonals, follow these steps:
1. Draw a straight line and label it AB, which will represent one of the sides of the parallelogram.
2. From point A, use a compass to draw an arc with a radius of 7.2 cm. Label the intersection point with the line AB as C.
3. Similarly, from point B, draw an arc with a radius of 5 cm. Label the intersection point with line AB as D.
- Note: The distances AC and BD represent the diagonal lengths of the parallelogram.
4. Draw a line segment CD, which will represent the other side of the parallelogram.
5. Measure the angle between the diagonals at point C. It should be 30 degrees.
- If required, use a protractor to measure the angle accurately.
6. Draw the line segment BC.
7. Extend line segment AB beyond point A and label the extension as E.
8. Use a compass to measure the distance CD and starting from point E, draw an arc that intersects line segment BC. Label the intersection point as F.
9. Connect points F and D to form the other side of the parallelogram.
- Note: Be sure to draw the line parallel to BC.
10. Finally, connect points A and D, and points B and C to complete the parallelogram ABCD.
Make sure to use a ruler throughout the construction to ensure accuracy.