Note: Your teacher will grade your response to ensure you receive proper credit for your answers. Given AB with a line overtop, explain how to construct a square with sides of length AB.

Answer 1

To construct a square with sides of length AB, follow these steps:

1. Start by drawing line segment AB.

2. Place your compass at point A and extend it to point B. Open the compass wider than half the length of AB and draw an arc above and below AB, intersecting it at points C and D. These points will be on the perpendicular bisector of AB.

3. Using the same compass width, place the compass at point C and draw an arc above AB. Similarly, place the compass at point D and draw an arc above AB. These arcs should intersect at point E.

4. Connect points A and D with a straight line segment. Similarly, connect points B and C with a straight line segment.

5. Finally, connect points E and D, and E and C to complete the square. The line segments created will have the same length, AB, forming a square.

By following these construction steps, you can create a square with sides of length AB.