To construct rectangle ABCD with the given dimensions, follow these steps:
Materials Needed:
- Ruler
- Compass
- Protractor
- Pencil
- Paper
Steps to Construct Rectangle ABCD:
1. Draw the Base:
- Start by drawing a horizontal line segment AB measuring 5.8 cm.
2. Locate Point C:
- At point A, use the protractor to draw a vertical line upwards.
- Place the compass at point A and draw an arc of 7.5 cm (the length of diagonal AC).
3. Find Point D:
- Without changing the compass width, place the compass at point B and draw another arc of 7.5 cm.
- The intersection of these two arcs defines point C.
4. Complete the Rectangle:
- Connect points A to C and B to D using straight lines.
- Ensure that lines AD and BC are perpendicular to line AB.
- Finally, connect points D and C to close the rectangle.
Verification:
- To confirm the rectangle's accuracy, check:
- Lengths: AB = 5.8 cm, AC = 7.5 cm.
- Use the Pythagorean theorem to verify that AD and BC equal 4.5 cm.
- Calculate using \( AC^2 = AB^2 + AD^2 \) (i.e., \( 7.5^2 = 5.8^2 + AD^2 \)).
Conclusion:
- You have successfully constructed rectangle ABCD with dimensions of 5.8 cm and diagonal 7.5 cm.