To construct a parallelogram given diagonals and the angle between them, follow these steps:
- Understanding dimensions: The diagonals of the parallelogram are 54 cm and 62 cm.
- Setting up your tools: You will need a ruler, a compass, and a protractor.
- Drawing the first diagonal: Use your ruler to draw a line segment of 54 cm (this will be diagonal AC).
- Finding the midpoint: Mark the midpoint of this segment, label it O.
- Drawing the second diagonal: From point O, draw a line of 62 cm at an angle of 70 degrees to the first diagonal (AC). Use your protractor for accuracy (this will be diagonal BD).
- Labeling points: Label the ends of the second diagonal as B and D.
- Completing the parallelogram: You now have points A, B, C, and D. Connect points A to B, B to D, and D to C using your ruler to complete the parallelogram ABCD.
- Verifying dimensions: Ensure that the opposite sides are equal (AB = CD and AD = BC) to ensure correctness. Also check if the angles between adjacent sides are 70 degrees.
This method ensures the parallelogram is constructed accurately based on the given dimensions and angle.